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# For a fundraising dinner, a florist is asked to create flowe

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Senior Manager
Joined: 21 Oct 2013
Posts: 414
For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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11 Apr 2014, 15:40
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For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
A) 4
B) 5
C) 6
D) 7
E) 8

OE:
Looking for (n + nC3) = 8
2 types of flower arrangements: some with 1 flower and some with 3 different flowers.
Therefore, total number of arrangements we could make from n different types of flowers = (n + nC3).
Since 4C3 = 4 (nC(n-1) always equals n combinations i.e. nC(n-1) = n), (n + nC3) = (4 + 4C3) = (4 + 4) = 8
Aim to get 8 distinct floral arrangements, 4 different types of flowers is the answer.

Hi, I want to know whether this reverse combination calculation is actually the GMAT style question, please.
Personally, I have never come across with this type of calculation.
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Posts: 56267
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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12 Apr 2014, 03:45
1
1
goodyear2013 wrote:
For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
A) 4
B) 5
C) 6
D) 7
E) 8

OE:
Looking for (n + nC3) = 8
2 types of flower arrangements: some with 1 flower and some with 3 different flowers.
Therefore, total number of arrangements we could make from n different types of flowers = (n + nC3).
Since 4C3 = 4 (nC(n-1) always equals n combinations i.e. nC(n-1) = n), (n + nC3) = (4 + 4C3) = (4 + 4) = 8
Aim to get 8 distinct floral arrangements, 4 different types of flowers is the answer.

Hi, I want to know whether this reverse combination calculation is actually the GMAT style question, please.
Personally, I have never come across with this type of calculation.

Yes, it is a GMAT style question. Below are bunch of similar questions to practice:

each-student-at-a-certain-university-is-given-a-four-charact-151945.html
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
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m04q29-color-coding-70074.html
a-researcher-plans-to-identify-each-participant-in-a-certain-134584-20.html

Hope this helps.
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Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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12 Apr 2014, 21:01
I don't understand the explanation.How do we arrive at the equation:$$n+C(n,3)=8$$?

If we take 8 different types of single flower bouquet then only we can have each table unique.

On the other hand,if we take 4 different types of flowers and decorate 4 tables with single flowers and the other four with different combinations of the 4 types of flowers won't the latter 4 tables essentially be familiar as the type of flowers remain the same irrespective of how we arrange them?

Bunuel,could you take on this one please?
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Posts: 32
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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13 Apr 2014, 04:41
1
AKG1593 wrote:
I don't understand the explanation.How do we arrive at the equation:$$n+C(n,3)=8$$?

If we take 8 different types of single flower bouquet then only we can have each table unique.

On the other hand,if we take 4 different types of flowers and decorate 4 tables with single flowers and the other four with different combinations of the 4 types of flowers won't the latter 4 tables essentially be familiar as the type of flowers remain the same irrespective of how we arrange them?

Bunuel,could you take on this one please?

Suppose you take n different type of flowers, so you can have n single flower bouquets.

C(n, 3) means number of unique combinations of 3 from n objects.
So, if n = 4, C (4, 3) = 4!/((4-3)!*3!) = 4

Also, we can have 4 unique combination of 3 flowers, hence all these 4 bouquets will be different from each other.
and with 4 different flowers we can make 4 different single flower bouquets

So, all together we will have 8 different type of bouquets

------------------------------------
Kudos if the answer helped
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Concentration: Finance
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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20 May 2014, 05:10
Let me see if I got this right. So we have 8 tables and we have two types of bouquet which can be either single flowers or a combination of three different flowers

If n=4

Then we can have 4c3 = 4 combinations of three different flowers plus 4 combinations if each of those flowers are used as single flowers.

Therefore 4+4=8

Hope this clarifies
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Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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26 Oct 2016, 07:16
goodyear2013 wrote:
For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
A) 4
B) 5
C) 6
D) 7
E) 8

I decided to try some "values", since we don't have to count that many options...
suppose we have 4 different types of flowers:
A
B
C
D
we already have covered 4 tables, if we put 1st option.
then, we need to select 3 of them for the 2nd option...
ABC
BCD
ACD
ABD
alternatively, 4C3, which is 4...
4+4 = 8
thus, with 4 types of flowers, we can cover all 8 tables so that no arrangement is repeated.
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Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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24 Feb 2018, 11:41
1
Hi All,

TESTing THE ANSWERS is a great way to tackle this type of question. You can also solve it using the Combination Formula and doing a bit of math.

Combinations = N!/K!(N-K)! Where N is the total number of items and K is the number of items in the 'subgroup'

The question asks to form 8 different flower bouquets using groups of flowers. We can make a bouquet with just 1 type of flower or 3 different types of flowers. We're asked for the LEAST number of different types of flowers needed to create 8 different bouquets.

With 4 different types of flower, we could have....

Bouquets with just 1 flower = 4c1 = 4!/(1!3!) = 4 different options

Bouquets with 3 different flowers = 4c3 = 4!/(3!1!) = 4 different options

Here, we have 4+4 = 8 different options, which is exactly what we're looking for. This MUST be the answer.

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Re: For a fundraising dinner, a florist is asked to create flowe   [#permalink] 24 Feb 2018, 11:41
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# For a fundraising dinner, a florist is asked to create flowe

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# FET based "zener amplifiers"

It is described as a negative power supply, where R1, R2, Q1 and Q2 form a current sink and Q3 "amplifies" the zener voltage, keeping a stable voltage between its drain (GND) and source (out).

So I have a few questions. I'll start just with the current sink. I've reduced it and isolated it as below:

1) Can I call the current sink configuration a series feedback pair?

I know it has the benefits of the high output impedance of the JFET, and the high gain of the BJT which allows a proper negative feedback. So the way I see it works like this. In initial conditions, Q2 gate is assumed at 0V, since there is still no current flowing through Q1. So Q2 will allow a $$\I_{DSS}\$$.

At the next moment, R2 will have a $$\V_{BE}\$$ across it from Q1 as long as $$\I_{Q2}*R2>0.7V\$$. That should be enough to keep Q1 saturated and R1 will set Q1 collector current. The voltage drop at R1 will set the voltage at Q2 gate.

2) Should Q1 be really saturated? I can't see other way, since there is really no restriction for its base current.

It is also clear how negative feedback works. If $$\I_D\$$ in Q2 tends to increase, $$\V_{BE}\$$ in Q1 tends to increase, also increasing Q1 collector current, that makes $$\V_{GS}\$$ more negative and regulates the disturbance.

R3 is the load and operating current in the example is $$\\frac{V_{BE}}{R2}\$$ , calculated for a 2.5mA renders $$\R = 269\Omega\$$.

J2 at left of the circuit is there just to check the actual $$\I_{DSS}\$$ for this part in LTspice, and that is equal to 5.19mA.

Simulations showed excellent results, ranging from R3 short circuited (green) up to 4.48k (pink). Last step was to 5.6k (not displayed below), that started to reach the compliance voltage.

3) How is it possible that $$\V_{GS,Q2}\$$ goes down to -14.5V and there is still current flowing through its drain and source?

According to this part datasheet: LSK489A, its pinch off voltage should be about -1.7V for a $$\V_{DS}\$$ of 10V at 25C. In my example, $$\V_{DS}\$$ ranges from -470mV for the 5.6k load to -14.3V for the short circuit. But any $$\V_{GS}\$$ more negative than ~ -1.7V should not allow the calculated current of 2.5mA in R2.

How is this possible and suggestions for fixing it, if needed. Changing R1? That still seems weird to me, because $$\V_{GS}\$$ and $$\I_{DS}\$$ are related by the

JFET basic equation: $$\ I_{DSS}(1-\frac{V_{GS}}{V_p})^2 \$$

Where $$\V_p\$$ is the pinch-off voltage.

So how is $$\V_{DS}\$$ of Q2 supposed to accomodate variations in voltage in order to keep the $$\I_{DS}\$$ when its $$\V_{GS}\$$ is being held by the voltage drop in R1?

I will elaborate further questions on the actual "zener amplified regulator".

EDIT1: fixed equations.

• I'm sure that the schematic is showing an N-channel MOSFET (enhancement type) not a JFET. And here you can find the analysis of a BJT's version electronics.stackexchange.com/questions/481308/…
– G36
Apr 11 '20 at 6:53
• Some considerations... Q3 does not amplify the Zener voltage; it acts as an "active diode" that follows this voltage by the help of a voltage-type negative feedback implemented by the Q2 voltage follower connecting the Q1 collector to its base. The high output impefance of Q2 is not because of the FET; it is due to the series negative feedback (R2 source degeneration). Q1 is not saturated; it works in active mode because of the voltage-type negative feedback. Visit also electronics.stackexchange.com/questions/483339/…. Apr 11 '20 at 10:25
• @G36, I understand, it caught my eyes as well. Doug Ford used this same symbol for JFETs all over this video. Since there is no standard for that, can't really call it wrong, despite JFET not having isolated gates as in his drawing. I get that a MOSFET should be used in Q3, but a JFET seems perfectly reasonable for the current sink, specially if one needs very low noise figures.
– tfm
Apr 11 '20 at 15:00
• For the JFET Doug Ford use a slightly different symbol.
– G36
Apr 11 '20 at 16:40

In order to drive a N-channel JFET into its saturation region, the following requirements must be met:

$$V_{GS} \le V_{GS(off)}$$

$$V_{DS} > V_{GS} - V_{GS(off)}$$

$$V_{GS} \le -1.17V \rightarrow fulfilled$$

$$-7.35 > -7.4V + 1.17V=-6.23V \rightarrow unfufilled$$

NOTE: $$\V_{GS(off)}=-1.17V\$$ comes from the model implementation. Right click on it and you can see its properties. All the other values comes from your first simulation.

EDIT #1

Although not the most elegant solution, if you still want to use a NJFET, you have to ensure that the drain voltage of the FET is not fixed by the $$\V_{FWD}\$$ of the BJT. I just added some random values, and you would have to optimize it:

EDIT #2

Here is a circuit similar to the one, shown in the video. (After watching the end of the video, I am almost sure that he is using a MOSFET instead of a JFET)

How it works

As you already explained, the components $$\R_G\$$, $$\M_1\$$, $$\Q1\$$ and $$\R_b\$$ form a controlled current sink. Disregarding the upper section for the moment, once the circuit is turned on, the source voltage of the MOSFET $$\M_1\$$ increases until it reaches $$\\approx 650mV\$$, thus turning on the BJT $$\Q_1\$$, which provides a negative feedback, which in turn reduces the $$\V_{GS}\$$ of the $$\M_1\$$.

There are two requiremts which must be fulfilled for the current source.

$$R_b > \frac{650mV}{I_{sink}}$$

AND

$$R_b > \frac{R_t\cdot 650mV}{V_{cc}-V_Z-650mV}$$

First condition ensures that there's enough current through $$\R_b\$$ to turn on $$\Q_1\$$, whereas the second one ensures that the voltage across $$\R_b\$$ is large enough to turn on $$\Q_1\$$.

The upper section of the circuit works as follows:

During start up the zener $$\D_1\$$ ensures that the gate voltage of $$\M_2\$$ is $$\\approx - V_Z = -4.7V\$$. At this moment the mosfet is on, and its source voltage starts to ramp ump until its $$\V_{GS} < V_{th}\$$ which yields an output voltage $$\V_{out}\approx -4.7V - V_{th} = -7V \$$

• @Hearth thanks for pointing that out :-) Apr 11 '20 at 11:19
• @vtolentino $V_{GS_{(OFF)}}$ equals vto in LTspice model, right? That would be -1.13V for this part, and datasheet shows a $V_{GS_{(OFF)max}}$ of -3.5V. So the reason there is current running through Q2, despite $V_{GS}$ at about -14V (well below the cut off voltage), is that the drain voltage is held approximately at the same voltage as the gate. For ex., using a 2.24k load, $V_{GS} = -8.84V$ and $V_{DS} = -8.74V$, so there is no reduction in substrate current. So based on that, I assume Q2 is not working as it should, in saturation region. How can I fix this still using a JFET?
– tfm
Apr 11 '20 at 16:48
• You cannot fix it because for a JFET the voltage at the gate needs to be lower than the voltage at the source. Thi is why you shoude use a MOSFET insted.
– G36
Apr 11 '20 at 17:21
• @HW_SW_Engineer exactly, $V_{to} = V_{GS_{OFF}}$. As for your second statement, it is wrong, because you are not considering the pinch off voltage, meaning $-8.74V < -8.74V + 1.17V = -7.67V$. I will updated my answer Apr 11 '20 at 17:23
• Understood it. Can I call this current sink configuration a series feedback pair?
– tfm
Apr 11 '20 at 17:51

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# Describe how the gravitational force between two objects depends on the distance between them.

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## The gravitational force F between two bodies of masses M and m kept at a distance d from each other is : Since gravitational force is inversely proportionalto the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces.Therefore , if we double the distance between two bodies, the gravitational force becomes one-fourth and if we halve the distance between two bodies, then the gravitational force becomes four times.

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# Gravitational force on point mass due to uniform rod

So we have a uniform rod of mass M and length L and we have placed a point mass of mass m, which is distance a away from the midpoint of the rod.

Now setting the coordiates axes to work with, I put the rod along the Y axis with its mid point coinciding with the Origin while the point mass m is put along the X axis a distance units away from the rod.

The point mass is P, and a differential mass element dm of the rod situated at y=length(OQ) where Q is the position of the mass element, is taken, and its corresponding force was found to be

$$\displaystyle{ d \vec{F} = \frac{G m dm} {{y}^{2}+{a}^{2}} (- cos \theta \hat{i} + sin \theta \hat{j}) }$$

where $$\theta$$ is the angle OPQ, Now using the linear mass density,

$$\displaystyle{ \frac{dm}{dx}=\frac{M}{L} }$$

and writing $$cos \theta$$ and $$sin \theta$$ in terms of y,

$$\displaystyle{ cos \theta = \frac{a}{\sqrt{{y}^{2}+{a}^{2}}} }$$

and

$$\displaystyle{ sin \theta = \frac{y}{\sqrt{{y}^{2}+{a}^{2}}} }$$

the Forces comes out to be,

$$\displaystyle{ {F}_{x} = - \frac{GmMa}{L} \int _{-\frac{L}{2}}^{\frac{L}{2}} { \frac{dy} {{({y}^{2}+{a}^{2})}^{\frac{3}{2}}} } }$$

and,

$$\displaystyle{ {F}_{y} = \frac{GmM}{L} \int _{-\frac{L}{2}}^{\frac{L}{2}} { \frac{y dy} {{({y}^{2}+{a}^{2})}^{\frac{3}{2}}} } }$$

Which gave the following results:

$$\displaystyle{ {F}_{y} = 0 }$$

as expected, due to the symmetry.

and,

$$\displaystyle{ {F}_{x} = - \frac{GmM}{a \sqrt{{a}^{2} + {(\frac{L}{2})}^{2}}} }$$

which I didn't expect to come out since I believe that if the it was assumed that the whole mass of the rod is concentrated at its mid point then the force should have been

$$\displaystyle{ {F}_{x} = - \frac{GmM}{{a}^{2}} }$$

So I am curious as to why or why not this result should follow.

• I've added the homework-and-exercises tag. In the future, please use this tag on this type of question. – user4552 Feb 16 '19 at 18:42
• @BenCrowell ok i will 👍 – Aditya Feb 16 '19 at 18:56

Newton invented integral calculus to prove the point mass premise for spherical objects. Gravitational force as a point mass is in general not valid for other shapes, although it is approximately true at large distances. At $$a>>L$$, your result approaches what you would expect.
Consider two forces of magnitude $$F$$ pulling on an object. If they pull at an angle $$\theta$$ to each other, the net magnitude will be $$\sqrt{(F + F\cos\theta)^2 + (F\sin\theta)^2} = F\sqrt{(1 + \cos\theta)^2 + \sin^2\theta} = F\sqrt{2+2\cos\theta}$$. As you can see, as the angle of separation increases, the force decreases. If the whole mass of the rod is concentrated at the midpoint, then the gravitational pull is all in one direction, leading to the greatest force. However, if the mass is spread out as in your scenario, gravitational pulls from different parts of the rod will be at different angles, making the net force weaker. In addition, some of the mass of the rod will be farther away from the point mass, which will weaken the pull as well. Sure enough, $$-\frac{GmM}{a\sqrt{a^2 + \big(\frac{L}{2}\big)^2}}$$ has a smaller absolute value than $$-\frac{GmM}{a^2}$$ because the denominator is larger when $$L > 0$$. As $$L$$ increases, the fraction will further decrease in magnitude because the gravitational pulls are at greater angles and portions of the mass are at even greater distances. So, this result makes perfect sense.


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# When the momentum of a proton is changed by an amount $p_{\circ}$, the corresponding change in de- Broglie wavelength is found to be $0.25 \%$. Then, the original momentum of the proton was

$\begin {array} {1 1} (a)\;p_{\circ} & \quad (b)\;100\: p_{\circ} \\ (c)\;400\: p_{\circ} & \quad (d)\;4\: p_{\circ} \end {array}$

Can you answer this question?

## 1 Answer

0 votes
Ans : (c)
$\lambda\: \sim\: \large\frac{1}{p}$
$\Rightarrow \large\frac{\Delta p}{p} = -\large\frac{ \Delta \lambda}{ \lambda}$
$\Rightarrow |\large\frac{ \Delta p}{p} | = | \large\frac{ \Delta \lambda}{ \lambda}|$
$\Rightarrow \large\frac{p_{\circ}}{p} = \large\frac{0.25}{100} = \large\frac{1}{400}$
$\Rightarrow p = 400p_{\circ}$

answered Dec 27, 2013
edited Mar 13, 2014

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# confusion on legendre symbol

i know that $\left(\frac{1}{2}\right)=1$ since $1^2\equiv 1 \pmod2$ now since $3\equiv 1\pmod2$ we should have $\left(\frac{3}{2}\right)=\left(\frac{1}{2}\right)=1$ but on Maple i get that $\left(\frac{3}{2}\right)=-1$ why?

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 The command \pmod produces the appropriate spacing and font for this. – joriki Mar 2 '12 at 9:17

Since the distinction is merely historic, I guess it makes sense for math software to treat them all the same; Wolfram|Alpha returns $-1$ for JacobiSymbol(3,2). See the Wikipedia article for the definition for even lower arguments; the interpretation that a value of $-1$ indicates a quadratic non-residue is no longer valid in this case.


text:
# Cosmology and Signals of Strongly Interacting Dark Sectors

Standard Model particles account for a small fraction of the matter content of the universe. If the remaining dark matter (DM) was ever in thermal equilibrium with itself or with the Standard Model (SM) sector, there must exist interactions that allowed its number density to be depleted to its present value. An interesting possibility for achieving this arises in scenarios where the DM is composed of pions'' of a QCD-like dark sector. The leading number changing process in these theories is the annihilation of three pions into two pions, which heats the pion bath relative to the SM. Consistency with observations of large and small scale structure in the universe requires a non-zero coupling with SM states, suggesting a multitude of experimental probes. I will review the cosmological production of DM in these strongly interacting dark sectors and discuss the prospects for discovering them at fixed target experiments.

Collection/Series:
Event Type:
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Event Date:
Tuesday, November 21, 2017 - 13:00 to 14:30
Location:
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Room #:
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# How many subgroups can we make of group whose order is a multiple of prime

If a group has $n$ elements of order $p$ ($p$ is prime) how many subgroups of order $p$ do we get? If the group was cyclic than only one unique subgroup of order $p$, but what if the group is non-cyclic?

-

Turn the question around: if $G$ has $m$ subgroups of order $p$, how many elements of order $p$ does it have?

If $x$ has order $p$, then so have $x^2,x^3,\dots,x^{p-1}$, and each of them generates the same subgroup of $G$, namely, $\langle x\rangle$. Thus, if $G$ has $m$ subgroups of order $p$, each of them must contain $p-1$ elements of order $p$, and since $p$ is prime, any two of these subgroups have trivial intersection. Thus, $G$ has $m(p-1)$ elements of order $p$.

So if $G$ has $n$ elements of order $p$, what is $m$ (in terms of $p$ and $n$)?

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thanks a lot for the help. –  d13 Oct 22 '12 at 11:08

Is the group itself of order p or are we discussing the order of the elements of this group?

Because if the group itself is of order p (i.e. size p) then there can only be two "subgroups." We can have a subgroup of size 1 (the identity group, {e}) and a subgroup of size p which is the same size as the original group.

This arises from Lagrange's Theorem:

Let G be a finite group and H a subgroup of G. Then the size of the subgroup divides the size of the group.

I take it that G can only have subgroups that divide it.

-
yes i understand what u say is right but the order of the group is not given, if it was, obviously i wouldn't ask the question here :) –  d13 Oct 23 '12 at 6:33


text: —–Visualize raw data – Extreme Value Analysis -Scatter plot matrix (less number of variables), heat map ? 2. Let n be the number of data values in the data set.The Median (Q2) is the middle value of the data set. Run this code in Google Colab Click Analyze from a Column data table, and then choose Identify outliers from the list of analyses for Column data. So what approach would you take, https://en.wikipedia.org/wiki/Tolerance_interval. These values affect the decision. Also, skim the literature for more ideas, e.g. | ACN: 626 223 336. Both Parametric as well as Non-Parametric approach could be used to identify outliers based on the characteristics of the underlying distribution. Should I include them in multivariate outlier detection process? … array=dataset.values The real SCADA data is a very noisy one because the technicians disconnects sensors and they are working several times at the year on the turbine generating many outliers. Evaluate the interquartile range (we’ll also be explaining these a bit further down). 5.Text Analytics , Image processing – No ? Using tukey formula to identify outlier The tukey formula uses quantiles to produce upper and lower range values beyond which all values are considered as outliers. The analysis is based on simple assumption that any value, too large or too small is outliers. Box plot use the IQR method to display data and outliers (shape of the data) but in order to be get a list of identified outlier, we will need to use the mathematical formula and retrieve the outlier data. Use the interquartile range. To better understand the implications of outliers better, I am going to compare the fit of a simple linear regression model on cars dataset with and without outliers. Q2 Thank you so much for your contribution. Make a box plot with dataset C. Then plot dataset B as separate series in the same chart (as a scatter … Try a suite of transforms and discover what works best on your project. i am going to remove some images (outliers) which are not related to my specific task. Assume that I have ~ 100k images which are used for training a Convolutional Neural Network and they were crawled by me. However, the same temperature in Bengaluru will not be considered unusual. Issue is the data is manually entered by someone so values are pretty random. Before you can remove outliers, you must first decide on what you consider to be an outlier. Data Preparation for Machine Learning. An outlier may be due to variability in the measurement or it may indicate an experimental error; the latter are sometimes excluded from … Can you assume a statistical distribution from which the observations were sampled or not (parametric or nonparametric)? Furthermore, can you also consider a comprehensive discussion on anomaly detection in time series data. … It depends on the data and chosen model. thanks for nice post. 2020-10-11 19:02:00 178,252 5638 53949. via the lofactor() function from the {DMwR} package: Local Outlier Factor (LOF) is an algorithm used to identify outliers by comparing the local density of a point with that of its neighbors, the outlierTest() from the {car} package gives the most extreme observation based on the given model and allows to test whether it is an outlier, in the {OutlierDetection} package, and; To exemplify, pattern differentials in a scatter plot is by far the most common method in identifying an outlier. Read more. For instance. https://machinelearningmastery.com/how-to-use-statistics-to-identify-outliers-in-data/. Q1 Context or rationale is required around decisions why a specific data instance is or is not an outlier. Outlier on the upper side = 3rd Quartile + 1.5 * IQR Outlier on the lower side = 1st Quartile – 1.5 * IQR The data that is different from other numbers in the given set is 81, The data that is different from other numbers in the given set is 52, Finding the Mode and Range from a Line Plot, Understanding the Mean Graphically: Two bars, Understanding the Mean Graphically: Four or more bars, Finding the Mean of a Symmetric Distribution, Computations Involving the Mean, Sample Size, and Sum of a Data Set, Finding the Value for a New Score that will yield a Given Mean, How Changing a Value Affects the Mean and Median, Choosing the Best Measure to Describe Data. There are also categorical variables in data. This will help you learn more about the problem and help you zoom into an approach and methods that work best for your specific case. — Boxplots. Basically defined as the number of standard deviations that the data point is away from the mean. We can straightway remove the outliers to get a proper trend. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. without using pca,and a person who is not expertise in that domain related to the datasets. Do these approaches work for my problem? I follow your blog in many topic. Then click Statistics and make sure the box next to Percentiles is checked. I recommend this process when working through new predictive modeling problems: A user born on 1984, buys 10 items of difference cumulative prices in June 2015, which again gets add up in next month, say July 2015. I describe and discuss the available procedure in SPSS to detect outliers. It can be, also statistical methods can be used: Extreme value analysis: This is the most basic form of detecting outliers. 2.Classification use cases – No ValueError: Unknown label type: ‘continuous’ Outliers are extreme values that fall a long way outside of the other observations. 2. I'm Jason Brownlee PhD Perhaps try some outlier detection algorithms, e.g. 2020-10-11 19:01:00 176,000 The procedure is described in the above tutorial. Do have any idea for removing outliers in my dataset? If i were to cluster to detect anomaly, how should I cluster each individual, and optimise the right number of clusters per individual iteratively? There are several methods that data scientists employ to identify outliers. Q1: Sure. or the other way around? If you identify an outlier in your data, you should examine the observation to understand why it is unusual and identify an appropriate remedy. To do that, I will calculate quartiles with DAX function PERCENTILE.INC, IQR, and lower, upper limitations. If you're seeing this message, it means we're having trouble loading external resources on our website. Boxplots are certainly one of the most common ways to visually identify outliers, but there are other graphs, such as scatterplots and individual value plots, to consider as well. Feature Selection, RFE, Data Cleaning, Data Transforms, Scaling, Dimensionality Reduction, The process of identifying outliers has many names in data mining and machine learning such as outlier mining, outlier modeling and novelty detection and anomaly detection. In his contributing chapter to Data Mining and Knowledge Discovery Handbook, Irad Ben-Gal proposes a taxonomy of outlier models as univariate or multivariate and parametric and nonparametric. Prism can perform outlier tests with as few as three values in a data set. and much more... great blog, I have few of your mini guides and really love them. By the way, your book may refer to the value of " 1.5×IQR" as being a "step". If this works, try to lift skill at detection using ML methods that use the simple tolerance intervals as inputs as well as other engineered features. —–Numeric input – Numeric Outpt -> uni-variate – Use Extreme Value Analysis (Scatter plot, histogran , box plot) I have a dataset (40K rows) which contains 4 categorical columns (more than 100 levels for two columns and around 20 levels for other two columns) and 1 numeric column. There are two common ways to do so: 1. Visualize the data using scatterplots, histograms and box and whisker plots and look for extreme values, Assume a distribution (Gaussian) and look for values more than 2 or 3 standard deviations from the mean or 1.5 times from the first or third quartile, Filter out outliers candidate from training dataset and assess your models performance, Use clustering methods to identify the natural clusters in the data (such as the k-means algorithm), Identify data instances that are a fixed distance or percentage distance from cluster centroids, Use projection methods to summarize your data to two dimensions (such as, Visualize the mapping and identify outliers by hand, Use proximity measures from projected values or codebook vectors to identify outliers. If the mean accurately represents the … Box Plots – in the image below you can see that several points exist outside of the box. Outliers can skew the summary distribution of attribute values in descriptive statistics like mean and standard deviation and in plots such as histograms and scatterplots, compressing the body of the data. I also want to implement the same in multivariate time series. Hi (leverage) A leverage (Hi) measures the distance from an observation's x-value to the average of the x-values for all observations … From Wikipedia. i am trying to train the dataset and this is the error, I am facing raise ValueError(“Unknown label type: %r” % y_type) Try both ways and see which results in the best performance. —–Numeric input – Numeric Outpt -> multivariate – Use PCA ?? No. Donate Login Sign up. Perhaps you could save the removed data as part of the filtering process? http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.Imputer.html#sklearn.preprocessing.Imputer. Sort of. If we subtract 1.5 x IQR from the first quartile, any data values that are less than this number are considered outliers. Plus there is no way of selectively removing the outliers. I tried using the scikit imputer in step 2.1 above but didn’t work ..any suggestions? Q2: That is a not a lot of data and it may be hard to know the structure of your data. Using Z score is another common method. Newsletter | Q2] Should we consider the skewness & kurtoisis distance to dealt with of categorical features which are encoded ? Box plots are a graphical depiction of numerical data through their quantiles. Welcome! Search for courses, skills, and videos. In this post, we will explain in detail 5 tools for identifying outliers in your data set: (1) histograms, (2) box plots, (3) scatter plots, (4) residual values, and (5) Cook’s distance. Statisticians have developed many ways to identify what should and shouldn't be called an outlier. Which approach do you suggest? I have a minute by minute data and total number of users of that particular minute how can i detect rate change in real time as of now i am doing it with z scores and comparing it with historical data but i am getting lots of false positives alerts. Q1] Should we only consider the outlier values of the target variable to be eliminated or should we eliminate the outlier values from other features as well if they are going to be used for prediction purposes ? How many models would that require? I have tried using Isolation forest and Local outlier factor method from Scikit learn and detected anomalies by them but I am not sure how did they detect those observations as anomalies. Twitter | For example, in a normal distribution, outliers may be values on the tails of the distribution. Do you have a suggestion for filtering outliers in a problem like this? Any help from your side will be highly appreciated. For instance, any Z-score obtained for a distribution comprising value greater than 3 or less than -3 is considered to be an outlier. Suppose that I don’t want to remove the outlier because it is an important data point. Maybe the origin of this, is because the prognosis of Wind turbines failures is a very unbalanced problem. Given that one of the biggest advantages of deep neural networks is that they perform they own feature selection under the hood, I’m curious about if they’re capable of dealing with outliers on their own as well. They’re always tricky to deal with! Extreme low values and extremely high values will be called as outliers. Hi Jason, still waiting for the tutorial on implementation of the outlier detection methods. Find the outlier(s) in the given data set below. You can use both visualizations and formulas to identify outliers in Excel. Some algorithms may perform better, such as linear methods. Thanks for sharing the article. Search. Let me illustrate this using the cars dataset. one-class prediction? Is outlier a separate machine learning technique? 550 200 35.5 2.5 1.6 2020-10-11 19:02:00 178,252. Even before predictive models are prepared on training data, outliers can result in misleading representations and in turn misleading interpretations of collected data. It measures the spread of the middle 50% of values. Even looking through introductory books on machine learning and data mining won’t be that useful to you. I recommend working through a stepped process from extreme value analysis, proximity methods and projection methods. Outliers are identified by assessing whether or not they fall within a set of numerical boundaries called "inner fences" and "outer fences". 1. Ltd. All Rights Reserved. So we identify three data sets now: A) Original dataset B) Dataset containing outliers only C) Dataset containing original data with outliers removed. Using graphs to identify outliers. One way to determine if outliers are present is to create a box plot for the dataset. You do not need to know advanced statistical methods to look for, analyze and filter out outliers from your data. Is it needed at all or just input outliers detection is needed? IDENTIFYING OUTLIERS. This is weird since I tested remove outliers with univariate, pca, denoisy autoencoder and all of them are in fact removing a big portion of the failures, that is a not wanted behaviour. Outliers in input data can skew and mislead the training process of machine learning algorithms resulting in longer training times, less accurate models and ultimately poorer results. Is neural network OK with having some inputs occasionally have value bigger than 1? Can you tell any application of outlier ranking? Identifying outliers in a stack of data is simple. Start by making some assumptions and design experiments where you can clearly observe the effects of the those assumptions against some performance or accuracy measure. E.g. Groupings include both the properties that are standard to any bill (account, region …) and customizable, user defined tags that are relevant to the business unit evaluating the outliers (owner, project, … column 'Vol' has all values around 12xx and one value is 4000 (outlier).. Now I would like to exclude those rows that have Vol column like this.. Outlier detection and imputation, which one should I do first? — Page 19, Data Cleaning, 2019. On scatterplots, points that are far away from others are possible outliers. For a newbie in ML and python your books just cut the crap and help me get started…. User selects outlier limit to identify outliers before doing ‘descriptive statistics and normality’. Thank you for the article , it help me more clear about the problem of how to manage outlier in training data set. Does output outlier detection proven to improve predictions results? An alternative strategy is to move to models that are robust to outliers. There is no precise way to define and identify outliers in general because of the specifics of each dataset. I’m not sure off hand. (By manually looking over the outlier data points doesn’t seems anomalous.) For a classical treatment of outliers by statisticians, check out: For a modern treatment of outliers by data mining community, see: Discover how in my new Ebook: Courses. Here are the statistical concepts that we will employ to find outliers: 1. Many machine learning algorithms are sensitive to the range and distribution of attribute values in the input data. Contact | Then the outliers will be the numbers that are between one and two steps from the hinges, and extreme value will be the … What is an Outlier? For example, a temperature reading of 32 degrees in a day in July in London will be considered too unusual. Often, it is easiest to identify outliers by graphing the data. Also, you can use an indication of outliers in filters and multiple visualizations. Practice identifying outliers using the 1.5*IQR rule. The outliers (marked with asterisks or open dots) are between the inner and outer fences, and the extreme values (marked with whichever symbol you didn't use for the outliers) are outside the outer fences. Try imputing with a mean, median or knn by hand as a starting point. Practice identifying outliers using the 1.5*IQR rule. In his book Outlier Analysis, Aggarwal provides a useful taxonomy of outlier detection methods, as follows: Aggarwal comments that the interpretability of an outlier model is critically important. Bojan Miletic asked a question about outlier detection in datasets when working with machine learning algorithms. A simple way to find an outlier is to examine the numbers in the data set. I think you have have outliers in all data types and I think it is not intuitive whether they will impact model performance or not. —–2.Some Algorithms itself robust to handle outlier , ex- decision tree, 3.Clustering use cases – Yes They are the extremely high or extremely low values in the data set. Hi, Time No_of_users Total_logging Total_token_request Identify outliers in Power BI with IQR method calculations By doing the math, it will help you detect outliers even for automatically refreshed reports. Start out simple with extreme value analysis. https://machinelearningmastery.com/start-here/#process. I hope to cover it in the future. There are robust forms of regression that minimize the median least square errors rather than mean (so-called robust regression), but are more computationally intensive. There are also methods like decision trees that are robust to outliers. I would like to know are these tools applicable for image type data. I want to select the most logical value in a month for that subscriber. 1.Regression (how many/much) use cases – Yes IQR or 15 beyond the quartiles. 553 195 30.5 2.5 1.6 2.1. Also thereis some information compression and also many missing data. I recommend testing a suite of methods and discover through careful experiment what works best for your dataset. Even though this has a little cost, filtering out outliers is worth it. RSS, Privacy | My data looks like below :-, Time No_of_users Now I know that certain rows are outliers based on a certain column value. If there are only numeric columns then it could be very easy by using these suggested methods to detect anomalies but having categorical variable, I am confused on how to select right approach. It is important to identify outliers because they can significantly affect your model, providing potentially misleading or incorrect results. So, essentially I need to put a filter on the data frame such that we select all rows where the values of a certain column are … Instead, you are a domain expert. Once you have explore simpler extreme value methods, consider moving onto proximity-based methods. Let’s get started with some statistics to find an outlier in Excel. P1 P2 P3 P4 H and I help developers get results with machine learning. Proximity based detection: Proximity based methods deal with the distance formula to identify outliers. Closing Thoughts. Describe the detailed procedure to identify the outlying patterns? I have little issue where it is relative to the global population, but do I model an anomaly detection where it is relative to the individual’s past behavior? It is a very … probabilistic tolerance intervals: So, just analyzing Revenue variable on its own i.e univariate analysis, we were able to identify 7 outlier candidates which dropped to 3 candidates when a bivariate analysis was performed. Set up a filter in your testing tool. (commonly 98 to 1% failures). Sorry, I don’t have exampels for anomaly detection in time series. —–Custer in high dimension – High-Dimensional Outlier Detection, 4.Recommendation use-cases – No (algorithm should be already robust to handle outliers ?). Projection methods are relatively simple to apply and quickly highlight extraneous values. I am trying to do Enron dataset problem of Udacity please help me how should i start. Does “feature extraction using pretrained CNN + clustering” work for my problem? Are you considered with outliers in one or more than one attributes (univariate or multivariate methods)? You could spot check some methods that are robust to outliers. The Data Preparation EBook is where you'll find the Really Good stuff. About the issue of outliers, from my real experience in real datasets like Wind turbines, the indentified as outliers tends to be the rows that indicates a failure, this means if you remove them you are removing the failure patterns(or target labeling) that you want to model. In other words, my CSV file looks like this Such numbers are known as outliers. Sir, On boxplots, Minitab uses an asterisk (*) symbol to identify outliers. Take my free 7-day email crash course now (with sample code). Also, sometimes termed as the univariate outlier. Thanks for the insight about outlier detection. In statistics, an outlier is an observation point that is distant from other observations. The ends drive the means, in this case. There is no one best way James, I’d encourage you to brainstorm a suite of approaches, test each. By breaking the outliers down using multiple, user-selected groupings we are able to identify outliers at a more granular level and provide more meaningful detailed drilldowns of associated billing line items. Because, it can drastically bias/change the fit estimates and predictions. i tried to rescale the data but still the problem persists. I have a pandas data frame with few columns. 3. Facebook | 552 201 35.5 2.5 -2.6 These models too perform the same function, i.e. Address: PO Box 206, Vermont Victoria 3133, Australia. I will evaluate accuracy of model If you have a question about machine learning, sign-up to the newsletter and reply to an email or use the contact form and ask, I will answer your question and may even turn it into a blog post. 3. How to Identify Outliers in your Data Outliers. Your language is easy to read understanding . Impute the Nan’s first If there are significant model accuracy benefits then there may be an opportunity to model and filter out outliers from your training data. Contextual outlier – A value being considered unusual given a specific context. Now I’m filtering by and expert-in-the-field method that is a manually defined ranges by the expert for each variable that excludes imposible values. Many machine learning algorithms are sensitive to the range and distribution of attribute values in the input... Outlier Modeling. You must interpret the raw observations and decide whether a value is an outlier or not. Y = array[:,3] Z-test or T-test are useful in performing this analysis. I have been working on a bit different dataset which is not binary (0,1) and not continuous. For example, in a... Get Started. These outliers are observations that are at least 1.5 times the interquartile range (Q3 – Q1) from the edge of the box. The interquartile range (IQR) is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) in a dataset. 2.2. then use your outlier function to remove outliers Anomaly Detection -Obvious yes, Here the problem stmt itself asks to identify anomaly /outlier, Note: where i am not certain , i put a question mark. Suggest how to solve this. A commonly used rule says that a data point is an outlier if it is more than 1.5\cdot \text {IQR} 1.5⋅IQR above the third quartile or below the first quartile. Once identified, outliers are separated from the original data. But yes, your approach sounds reasonable. scholar.google.com. Here are some examples that illustrate the view of outliers with graphics. 6. When plotting a chart the analyst can clearly see that something different exists. detecting them a… How to Identify Outliers in Python. imagine if you have ‘n’ numeric predictors, numeric target and each of them have Na’s / Nan’s in the range of 40-60% values…and lots of outliers To do so, click the Analyze tab, then Descriptive Statistics, then Explore: In the new window that pops up, drag the variable income into the box labelled Dependent List. One of the best ways to identify outliers data is by using charts. thank you for sharing. As of now we are doing this on just one data point but we are thinking of adding more values and correlating it. The Lower quartile (Q1) is the median of the lower half of the data set The Upper quartile (Q3) is the median of the upper half of the data set. Try removing the header line from the file? The box is the central tendency … Main … These values also called as noise in a dataset. Click to sign-up and also get a free PDF Ebook version of the course. If I keep outliers in my data after scaled it using scikit-learn’s Robust Scaler, I noticed that the outliers will have value bigger than 1. Plot for the dataset 100k images which are encoded ( by manually looking over the outlier detection (... To cover anomaly detection in the input... outlier Modeling be hard know! Far away from others are possible outliers with of categorical features which are encoded on simple that! Or more than one attributes ( univariate or multivariate methods ) best performance should n't called... Opportunity to model and filter out outliers is worth it ML and python your books just cut crap! View the data point but we are thinking of adding more values and high! Working through a stepped process from extreme value analysis, proximity methods and discover what best. A pandas data frame with few columns or just input outliers detection is?. To manage outlier in training data set through their quantiles 2.2. then use outlier. ( 0,1 ) and not all but the data Preparation Ebook is where you find. Consider moving onto proximity-based methods selectively removing the outliers examination of a boxplot models perform! Point is away from others are possible outliers it as point outlier data point the 1.5 * IQR.! Describe the detailed procedure to identify outliers once how to identify outliers, outliers are data that. Way James, i ’ d encourage you to brainstorm a how to identify outliers of approaches, test each of please. In time series data books just cut the crap and help me get started… method in an. Are the statistical concepts that we will employ to find an outlier an! Web filter, please make sure that the data set methods like decision that. The original data points doesn ’ t fit the pattern of rest of the outlier detection process can remove. Hard to know Advanced statistical methods can be used to identify outliers data is by using charts data! Also want to select the most logical value in a scatter plot by... Distribution comprising value greater than 3 or less than this number are considered.! A distribution comprising value greater than 3 or less than -3 is considered outlier concerning most observations a... The future Column data table, and a person who is not (. As the number of standard deviations that the data Preparation Ebook is where you 'll the. Pdf Ebook version of the box is the middle 50 % of values is considered outlier most! The range and distribution of attribute values in the future your outlier function the quartile... What you consider writing a mini-book actually showing implementation of any or all of the other around! Standard deviations that the post helped my data looks like below: -, No_of_users..., still waiting for the tutorial on implementation of any or all of underlying... In SPSS to detect outliers lot of data values in the data point is from. Not expertise in that domain related to my specific task once you have simpler! Most basic form of detecting outliers 'm Jason Brownlee PhD and i help developers get results with machine learning data. Plots – in the input... outlier Modeling both ways and see which results in the data which not... Would be a good start this number are considered outliers some examples that illustrate the view of with... Research put into outlier detection process projection methods and see which results the. In general because of the data point but we are doing this on just one point! Just cut the crap and help me get started… middle value of the other around. On identifying outlier data values in the input data approaches, test each features... Specific data instance is or is not an outlier outlier Modeling are observations that are to... Manually looking how to identify outliers the outlier data points doesn ’ t seems anomalous., first multiply. When working with machine learning and data mining won ’ t want to remove some images ( )... To the range and distribution of attribute values in the given data set there also. A stepped process from extreme value methods, consider moving onto proximity-based methods a temperature reading of 32 in! Same months can have multiple entries Beginner to Advanced course to improve your fast! ‘ relative to ’ it when loading or just input outliers detection is needed dataset which is expertise... By manually looking over the outlier because it is a useful way to define and identify.. Perform the same function, i.e to Percentiles is checked filtering process ways... Employ to find the Really good stuff research put into outlier detection in datasets when through. Outliers based on the characteristics of the numbers in the input... outlier.... Also many missing data my problem the ways you described below by far the most basic form of detecting.. To remove the outlier in training data, outliers may be hard to know the structure of data. Specific context bounds of our data range these outliers are extreme values that fall a long outside. Assume a statistical distribution from which the observations were sampled or not because, it we... Bias/Change the fit estimates and predictions experiment what works best for your data number! Code ) an indication of outliers in Excel a simple way to structure methods on! ( 0,1 ) and not continuous so: 1 a Column data upper. Anomaly detection in datasets when working with machine learning and data mining won ’ fit... We will employ to find the outlier detection proven to improve predictions results should should... Out outliers from the mean the specifics of each dataset * ) to... This topic, i ’ d encourage you to brainstorm a suite of methods and methods... The extreme values that are less than -3 is considered to be an outlier in.. Months and not continuous point outlier the original data some statistics to find outlier... Are considered outliers great Master Excel Beginner to Advanced course to improve predictions results are encoded sharing. Before you can codify the expert method using statistics – e.g the interval –13! Extremely high or extremely low values and extremely high or extremely low values and extremely high or low! Does output outlier detection process out outliers from your training data, outliers may be hard to know Advanced methods. 50 input features and 1 target variable in July in London will be highly appreciated multiple... Me how should i start lower bounds of our data range data Preparation Ebook is where you 'll the! A useful way to find an outlier is to examine the numbers in data! They were crawled by me T-test are useful in performing this analysis with of categorical features are! On a certain Column value from centroid would be a good start T-test are useful in performing this.! You have explore simpler extreme value analysis, proximity methods and discover through careful experiment what best... Step '' useful in performing this analysis are relatively simple to apply and quickly highlight values., the same function, i.e and correlating it save the removed data as part the... Misleading interpretations of collected data 5000 52000 2020-10-11 19:02:00 178,252 set of values for more,. Detection process inputs occasionally have value bigger than 1 an important data point but we are doing this on one. Are extreme values that fall a long way outside of the course we will employ to find an or. Of 32 degrees in a feature, we call it as point outlier of,... Set.The Median ( q2 ) is the data point but we are doing this on just data... Occasionally have value bigger than 1 or more than one attributes ( univariate or multivariate methods ) it be... Data looks like below: -, time No_of_users Total_logging Total_token_request 2020-10-11 19:01:00 176,000 5000 52000 19:02:00. Define and identify outliers '' as being a  step '' standard deviations that the Preparation... Noise in a month for that subscriber loading external resources on our website their quantiles Median ( q2 ) the! Topic, i will calculate quartiles with DAX function PERCENTILE.INC, IQR, and then choose identify.... Work for my problem Really good stuff using pretrained CNN + clustering ” work for my problem where. Waiting for the article, it can drastically bias/change the fit estimates and predictions idea for removing outliers the... And projection methods do have any idea for removing outliers in my dataset also consider a comprehensive on! It lifts model skill on your specific dataset simpler extreme value analysis: this is not... Dataset problem of how to detect the outliers to get a free PDF Ebook version of the underlying distribution,! Is known about the problem of how to view the data set.The Median ( q2 ) is the data... 0,1 ) and not all but the data set below or nonparametric ) your outlier.! Have any idea for removing outliers in my dataset clustering ” work for my problem with as few as values... Decision trees that are less than this number are considered outliers outliers with graphics instance any..., and a person who is how to identify outliers an outlier there are several methods that robust! Effectively ‘ relative to ’ by far how to identify outliers most logical value in month... Would like to know are these tools applicable for image type data this case brainstorm a suite of and. Type data and make sure the box the distribution use your outlier function distant other. Were crawled by me comprising value greater than 3 or less than this number are outliers! The way, your book may refer to the datasets fit the pattern of rest of filtering. On your specific dataset is in millions am going to remove outliers, you interpret.


text:
# 2.5 Assignment 2

## Detecting Flu Epidemics via Search Engine Query Data

Flu epidemics constitute a major public health concern causing respiratory illnesses, hospitalizations, and deaths. According to the National Vital Statistics Reports published in October 2012, influenza ranked as the eighth leading cause of death in 2011 in the United States. Each year, 250,000 to 500,000 deaths are attributed to influenza related diseases throughout the world.

The U.S. Centers for Disease Control and Prevention (CDC) and the European Influenza Surveillance Scheme (EISS) detect influenza activity through virologic and clinical data, including Influenza-like Illness (ILI) physician visits. Reporting national and regional data, however, are published with a 1-2 week lag.

The Google Flu Trends project was initiated to see if faster reporting can be made possible by considering flu-related online search queries – data that is available almost immediately.

## Problem 1.1 - Understanding the Data

We would like to estimate influenza-like illness (ILI) activity using Google web search logs. Fortunately, one can easily access this data online:

ILI Data - The CDC publishes on its website the official regional and state-level percentage of patient visits to healthcare providers for ILI purposes on a weekly basis.

Google Search Queries - Google Trends allows public retrieval of weekly counts for every query searched by users around the world. For each location, the counts are normalized by dividing the count for each query in a particular week by the total number of online search queries submitted in that location during the week. Then, the values are adjusted to be between 0 and 1.

The csv file FluTrain (CSV) aggregates this data from January 1, 2004 until December 31, 2011 as follows:

“Week” - The range of dates represented by this observation, in year/month/day format.

“ILI” - This column lists the percentage of ILI-related physician visits for the corresponding week.

“Queries” - This column lists the fraction of queries that are ILI-related for the corresponding week, adjusted to be between 0 and 1 (higher values correspond to more ILI-related search queries).

Before applying analytics tools on the training set, we first need to understand the data at hand. Load “FluTrain.csv” into a data frame called FluTrain. Looking at the time period 2004-2011, which week corresponds to the highest percentage of ILI-related physician visits? Select the day of the month corresponding to the start of this week.

 Exercise 1    January February March April May June July August September October November December  October Exercise 2    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  18 Exercise 3    2004 2005 2006 2007 2008 2009 2010 2011  2009

Explanation

We can limit FluTrain to the observations that obtain the maximum ILI value with subset(FluTrain, ILI == max(ILI)). From here, we can read information about the week at which the maximum was obtained. Alternatively, you can use which.max(FluTrain$ILI) to find the row number corresponding to the observation with the maximum value of ILI, which is 303. Then, you can output the corresponding week using FluTrain$Week[303].

Which week corresponds to the highest percentage of ILI-related query fraction?

 Exercise 4    January February March April May June July August September October November December  October Exercise 5    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31  18 Exercise 6    2004 2005 2006 2007 2008 2009 2010 2011  2009 CheckShow Answer

Explanation

We can limit FluTrain to the observations that obtain the maximum ILI value with subset(FluTrain, Queries == max(Queries)). From here, we can read information about the week at which the maximum was obtained. Alternatively, you can use which.max(FluTrain$Queries) to find the row number corresponding to the observation with the maximum value of Queries, which is 303. Then, you can output the corresponding week using FluTrain$Week[303].

## Problem 1.2 - Understanding the Data

Let us now understand the data at an aggregate level. Plot the histogram of the dependent variable, ILI. What best describes the distribution of values of ILI?

Exercise 7

Most of the ILI values are small, with a relatively small number of much larger values (in statistics, this sort of data is called “skew right”).

The ILI values are balanced, with equal numbers of unusually large and unusually small values.

Most of the ILI values are large, with a relatively small number of much smaller values (in statistics, this sort of data is called “skew left”).

Explanation

The histogram of ILI can be obtained with hist(FluTrain$ILI). Visually, the data is skew right. CheckShow Answer ## Problem 1.3 - Understanding the Data When handling a skewed dependent variable, it is often useful to predict the logarithm of the dependent variable instead of the dependent variable itself – this prevents the small number of unusually large or small observations from having an undue influence on the sum of squared errors of predictive models. In this problem, we will predict the natural log of the ILI variable, which can be computed in R using the log() function. Plot the natural logarithm of ILI versus Queries. What does the plot suggest?. Exercise 8 There is a negative, linear relationship between log(ILI) and Queries. There is no apparent linear relationship between log(ILI) and Queries. There is a positive, linear relationship between log(ILI) and Queries. Explanation The plot can be obtained with plot(FluTrain$Queries, log(FluTrain$ILI)). Visually, there is a positive, linear relationship between log(ILI) and Queries. CheckShow Answer ## Problem 2.1 - Linear Regression Model Based on the plot we just made, it seems that a linear regression model could be a good modeling choice. Based on our understanding of the data from the previous subproblem, which model best describes our estimation problem? Exercise 9 ILI = intercept + coefficient x Queries, where the coefficient is negative Queries = intercept + coefficient x ILI, where the coefficient is negative ILI = intercept + coefficient x Queries, where the coefficient is positive Queries = intercept + coefficient x ILI, where the coefficient is positive log(ILI) = intercept + coefficient x Queries, where the coefficient is negative Queries = intercept + coefficient x log(ILI), where the coefficient is negative log(ILI) = intercept + coefficient x Queries, where the coefficient is positive Queries = intercept + coefficient x log(ILI), where the coeffcient is positive Explanation From the previous subproblem, we are predicting log(ILI) using the Queries variable. From the plot in the previous subproblem, we expect the coefficient on Queries to be positive. CheckShow Answer ## Problem 2.2 - Linear Regression Model Let’s call the regression model from the previous problem (Problem 2.1) FluTrend1 and run it in R. Hint: to take the logarithm of a variable Var in a regression equation, you simply use log(Var) when specifying the formula to the lm() function. What is the training set R-squared value for FluTrend1 model (the “Multiple R-squared”)? Exercise 10 Numerical Response Explanation The model can be trained with: FluTrend1 = lm(log(ILI)~Queries, data=FluTrain) From summary(FluTrend1), we read that the R-squared value is 0.709. CheckShow Answer ## Problem 2.3 - Linear Regression Model For a single variable linear regression model, there is a direct relationship between the R-squared and the correlation between the independent and the dependent variables. What is the relationship we infer from our problem? (Don’t forget that you can use the cor function to compute the correlation between two variables.) Exercise 11 R-squared = Correlation^2 R-squared = log(1/Correlation) R-squared = exp(-0.5Correlation) Explanation To test these hypotheses, we first need to compute the correlation between the independent variable used in the model (Queries) and the dependent variable (log(ILI)). This can be done with Correlation = cor(FluTrain$Queries, log(FluTrain$ILI)) The values of the three expressions are then: Correlation^2 = 0.7090201 log(1/Correlation) = 0.1719357 exp(-0.5Correlation) = 0.6563792 It appears that Correlation^2 is equal to the R-squared value. It can be proved that this is always the case. Note that the “exp” function stands for the exponential function. The exponential can be computed in R using the function exp(). CheckShow Answer ## Problem 3.1 - Performance on the Test Set The csv file FluTest.csv provides the 2012 weekly data of the ILI-related search queries and the observed weekly percentage of ILI-related physician visits. Load this data into a data frame called FluTest. Normally, we would obtain test-set predictions from the model FluTrend1 using the code PredTest1 = predict(FluTrend1, newdata=FluTest) However, the dependent variable in our model is log(ILI), so PredTest1 would contain predictions of the log(ILI) value. We are instead interested in obtaining predictions of the ILI value. We can convert from predictions of log(ILI) to predictions of ILI via exponentiation, or the exp() function. The new code, which predicts the ILI value, is PredTest1 = exp(predict(FluTrend1, newdata=FluTest)) What is our estimate for the percentage of ILI-related physician visits for the week of March 11, 2012? (HINT: You can either just output FluTest$Week to find which element corresponds to March 11, 2012, or you can use the “which” function in R. To learn more about the which function, type “?which” in your R console.)

Exercise 12

Numerical Response

Explanation

To obtain the predictions, we need can run

PredTest1 = exp(predict(FluTrend1, newdata=FluTest))

Next, we need to determine which element in the test set is for March 11, 2012. We can determine this with:

## Problem 3.3 - Performance on the Test Set

What is the Root Mean Square Error (RMSE) between our estimates and the actual observations for the percentage of ILI-related physician visits, on the test set?

Exercise 14

Numerical Response

Explanation

The RMSE can be calculated by first computing the SSE:

SSE = sum((PredTest1-FluTest$ILI)^2) and then dividing by the number of observations and taking the square root: RMSE = sqrt(SSE / nrow(FluTest)) Alternatively, you could use the following command: sqrt(mean((PredTest1-FluTest$ILI)^2)).

## Problem 4.1 - Training a Time Series Model

The observations in this dataset are consecutive weekly measurements of the dependent and independent variables. This sort of dataset is called a “time series.” Often, statistical models can be improved by predicting the current value of the dependent variable using the value of the dependent variable from earlier weeks. In our models, this means we will predict the ILI variable in the current week using values of the ILI variable from previous weeks.

First, we need to decide the amount of time to lag the observations. Because the ILI variable is reported with a 1- or 2-week lag, a decision maker cannot rely on the previous week’s ILI value to predict the current week’s value. Instead, the decision maker will only have data available from 2 or more weeks ago. We will build a variable called ILILag2 that contains the ILI value from 2 weeks before the current observation.

To do so, we will use the “zoo” package, which provides a number of helpful methods for time series models. While many functions are built into R, you need to add new packages to use some functions. New packages can be installed and loaded easily in R, and we will do this many times in this class. Run the following two commands to install and load the zoo package. In the first command, you will be prompted to select a CRAN mirror to use for your download. Select a mirror near you geographically.

install.packages(“zoo”)

library(zoo)

After installing and loading the zoo package, run the following commands to create the ILILag2 variable in the training set:

ILILag2 = lag(zoo(FluTrain$ILI), -2, na.pad=TRUE) FluTrain$ILILag2 = coredata(ILILag2)

In these commands, the value of -2 passed to lag means to return 2 observations before the current one; a positive value would have returned future observations. The parameter na.pad=TRUE means to add missing values for the first two weeks of our dataset, where we can’t compute the data from 2 weeks earlier.

How many values are missing in the new ILILag2 variable?

Exercise 15

Numerical Response

Explanation

This can be read from the output of summary(FluTrain$ILILag2). CheckShow Answer ## Problem 4.2 - Training a Time Series Model Use the plot() function to plot the log of ILILag2 against the log of ILI. Which best describes the relationship between these two variables? Exercise 16 There is a strong negative relationship between log(ILILag2) and log(ILI). This is a weak or no relationship between log(ILILag2) and log(ILI) There is a strong positive relationship between log(ILILag2) and log(ILI). Explanation From plot(log(FluTrain$ILILag2), log(FluTrain$ILI)), we observe a strong positive relationship. CheckShow Answer ## Problem 4.3 - Training a Time Series Model Train a linear regression model on the FluTrain dataset to predict the log of the ILI variable using the Queries variable as well as the log of the ILILag2 variable. Call this model FluTrend2. Which coefficients are significant at the p=0.05 level in this regression model? (Select all that apply.) Exercise 17 Intercept Queries log(ILILag2) What is the R^2 value of the FluTrend2 model? Exercise 18 Numerical Response Explanation The following code builds and summarizes the FluTrend2 model: FluTrend2 = lm(log(ILI)~Queries+log(ILILag2), data=FluTrain) summary(FluTrend2) As can be seen, all three coefficients are highly significant, and the R^2 value is 0.9063. CheckShow Answer ## Problem 4.4 - Training a Time Series Model On the basis of R-squared value and significance of coefficients, which statement is the most accurate? Exercise 19 Due to overfitting, FluTrend2 is a weaker model then FluTrend1 on the training set. FluTrend2 is about the same quality as FluTrend1 on the training set. FluTrend2 is a stronger model than FluTrend1 on the training set. Explanation Moving from FluTrend1 to FluTrend2, in-sample R^2 improved from 0.709 to 0.9063, and the new variable is highly significant. As a result, there is no sign of overfitting, and FluTrend2 is superior to FluTrend1 on the training set. CheckShow Answer ## Problem 5.1 - Evaluating the Time Series Model in the Test Set So far, we have only added the ILILag2 variable to the FluTrain data frame. To make predictions with our FluTrend2 model, we will also need to add ILILag2 to the FluTest data frame (note that adding variables before splitting into a training and testing set can prevent this duplication of effort). Modify the code from the previous subproblem to add an ILILag2 variable to the FluTest data frame. How many missing values are there in this new variable? Exercise 20 Numerical Response Explanation We can add the new variable with: ILILag2 = lag(zoo(FluTest$ILI), -2, na.pad=TRUE)

FluTest$ILILag2 = coredata(ILILag2) From summary(FluTest$ILILag2), we can see that we’re missing two values of the new variable.

## Problem 5.2 - Evaluating the Time Series Model in the Test Set

In this problem, the training and testing sets are split sequentially – the training set contains all observations from 2004-2011 and the testing set contains all observations from 2012. There is no time gap between the two datasets, meaning the first observation in FluTest was recorded one week after the last observation in FluTrain. From this, we can identify how to fill in the missing values for the ILILag2 variable in FluTest.

Which value should be used to fill in the ILILag2 variable for the first observation in FluTest?

Exercise 21

The ILI value of the second-to-last observation in the FluTrain data frame.

The ILI value of the last observation in the FluTrain data frame.

The ILI value of the first observation in the FluTest data frame.

The ILI value of the second observation in the FluTest data frame.

Explanation

The time two weeks before the first week of 2012 is the second-to-last week of 2011. This corresponds to the second-to-last observation in FluTrain.

Which value should be used to fill in the ILILag2 variable for the second observation in FluTest?

Exercise 22

The ILI value of the second-to-last observation in the FluTrain data frame.

The ILI value of the last observation in the FluTrain data frame.

The ILI value of the first observation in the FluTest data frame.

The ILI value of the second observation in the FluTest data frame.

Explanation

The time two weeks before the second week of 2012 is the last week of 2011. This corresponds to the last observation in FluTrain.

## Problem 5.3 - Evaluating the Time Series Model in the Test Set

Fill in the missing values for ILILag2 in FluTest. In terms of syntax, you could set the value of ILILag2 in row “x” of the FluTest data frame to the value of ILI in row “y” of the FluTrain data frame with “FluTest$ILILag2[x] = FluTrain$ILI[y]”. Use the answer to the previous questions to determine the appropriate values of “x” and “y”. It may be helpful to check the total number of rows in FluTrain using str(FluTrain) or nrow(FluTrain).

Explanation

From nrow(FluTrain), we see that there are 417 observations in the training set. Therefore, we need to run the following two commands:

FluTest$ILILag2[1] = FluTrain$ILI[416]

FluTest$ILILag2[2] = FluTrain$ILI[417]

What is the new value of the ILILag2 variable in the first row of FluTest?

Exercise 23

Numerical Response

Explanation

This can be read from FluTest$ILILag2[1]. What is the new value of the ILILag2 variable in the second row of FluTest? Exercise 24 Numerical Response Explanation This can be read from FluTest$ILILag2[2].

## Problem 5.4 - Evaluating the Time Series Model in the Test Set

Obtain test set predictions of the ILI variable from the FluTrend2 model, again remembering to call the exp() function on the result of the predict() function to obtain predictions for ILI instead of log(ILI).

What is the test-set RMSE of the FluTrend2 model?

Exercise 25

Numerical Response

Explanation

We can obtain the test-set predictions with:

PredTest2 = exp(predict(FluTrend2, newdata=FluTest))

And then we can compute the RMSE with the following commands:

SSE = sum((PredTest2-FluTest$ILI)^2) RMSE = sqrt(SSE / nrow(FluTest)) Alternatively, you could use the following command to compute the RMSE: sqrt(mean((PredTest2-FluTest$ILI)^2)).

The test-set RMSE of FluTrend2 is 0.294.

## Problem 5.5 - Evaluating the Time Series Model in the Test Set

Which model obtained the best test-set RMSE?

Exercise 26

FluTrend1

FluTrend2

Explanation

The test-set RMSE of FluTrend2 is 0.294, as opposed to the 0.749 value obtained by the FluTrend1 model.

In this problem, we used a simple time series model with a single lag term. ARIMA models are a more general form of the model we built, which can include multiple lag terms as well as more complicated combinations of previous values of the dependent variable. If you’re interested in learning more, check out “?arima” or the available online tutorials for these sorts of models.

#### Learning Resource Types

theaters Lecture Videos
notes Lecture Notes
assignment_turned_in Problem Sets with Solutions


text:
# \scriptstyle placement fine tuning

I need a functional composition operator. I find \circ too big for it, so I've declared a math operator (within the amsart documentclass) as \scriptstyle\circ instead; the size is exactly what I would like to have but the placement seems wrong now, it is too low.

Does anybody know a simple way (without too many \raises and boxes) to place the symbol slightly higher?

Try with defining a new command \smallcirc

\newcommand{\smallcirc}{\mathbin{\text{\raisebox{0.2ex}{\scalebox{0.6}{$\circ$}}}}}

MWE:

\documentclass{amsart}
\usepackage{graphicx}
\newcommand{\smallcirc}{\mathbin{\text{\raisebox{0.2ex}{\scalebox{0.6}{$\circ$}}}}}

\begin{document}
$f\circ\alpha \quad\text{vs}\quad f\smallcirc\alpha$

$f \smallcirc \alpha_{f \smallcirc \alpha_{f \smallcirc \alpha}}$
\end{document}

Note that, defining the command with a \scripstyle in it, it's not a good idea since if you have that symbol in a sub/superscript, its size will remain the same as the one in display style.

• Thanks a lot! I preferred this one since it is more concise, more customizable, and works without graphicx too :D – მამუკა ჯიბლაძე Mar 19 '15 at 10:50
• Oops maybe it still needs graphicx - I load tikz and that I think loads graphicx... Well anyway – მამუკა ჯიბლაძე Mar 19 '15 at 10:52
• @მამუკაჯიბლაძე You're welcome. And, yes, tikz loads graphicx. – karlkoeller Mar 19 '15 at 10:54

Here's an answer that will work even in sub/superscript:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\centeredcirc}[1]{\vcenter{\hbox{$#1\circ$}}}
\newcommand{\smallcirc}{\mathbin{\mathchoice{\centeredcirc\scriptstyle}{\centeredcirc\scriptstyle}{\centeredcirc\scriptscriptstyle}{\centeredcirc\scriptscriptstyle}}}

\begin{document}

$f\circ\alpha \quad\text{vs}\quad f\smallcirc\alpha$
$g^{f\circ\alpha} \quad\text{vs}\quad g^{f\smallcirc\alpha}$

\end{document}

The following example uses the scaling method of karlkoeller's answer and enhances it in several ways:

• The new symbol is correctly vertically centered around the math axis.
• The side bearings are restored (heuristic).
• The scaling diminishes the line width. This is compensated by additionally stroking the symbol with an estimated line width to compensate the scaling.

Full example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{color}
\usepackage{graphicx}
\usepackage{pdfrender}

\makeatletter
\newcommand*{\smallcirc}{%
\mathbin{%
\mathpalette\@smallcirc{}%
}%
}
\newcommand*{\smallcircscale}{.6}
\newcommand*{\@smallcirc}[2]{%
% #1: math style
% #2: unused
\sbox0{$#1\vcenter{}$}% \ht0: math axis
\sbox2{$#1\circ\m@th$}%
% Calculate symbol width with original side bearings
% (in the hope, the symbol height is correct).
% The radius is estimated as symbol height minus math axis
% (\ht2 - \ht0).
\dimen@=\dimexpr
\smallcircscale\dimexpr2\ht2-2\ht0\relax
+ \wd2-2\ht2+2\ht0
\relax
% Estimated line thickness from symbol height
\dimen2=.1\ht2
% Calculate line width for rendering mode "Stroke".
\dimen2=\dimexpr\dimen2 - \smallcircscale\dimen2\relax
\raise\ht0\hbox to \dimen@{%
\hfil
\textpdfrender{
TextRenderingMode=FillStroke,
LineWidth=\dimen2,
}{%
\scalebox{\smallcircscale}{%
\lower\ht0\hbox{%
$#1\circ\m@th$%
}%
}%
}%
\hfil
}%
}
\makeatother

\begin{document}
\begin{align*}
\text{styles: }&
\scriptscriptstyle f \smallcirc \alpha
\\
\text{{\fontfamily{lmvtt}\selectfont\textbackslash circ}: }&
\scriptscriptstyle f \circ \alpha
\\
\text{axis: }&
\sbox0{${-}{\smallcirc}{-}$}
\rlap{\copy0}%
\vcenter{%
\hbox{%
\textcolor{red}{%
\vrule width\wd0 height .05pt depth .05pt\relax
}%
}%
}
\end{align*}
\end{document}


text:
# Korea and Koalas

Back home. Fortunately!

Even I can get tired of spicy food if it amounts to several dozens of cloves of garlic and more than four or five ounces of pepper paste every day and night. You see, I've tried to compensate for the complete lack of vegetables and side-dishes by an increased consumption of garlic (and pepper paste). Hmm...fortunately there's kimchi.

Kimchi's the national Korean food and consists of a few lonely leaves of lettuce heavily pickeled in vinegared garlic and pepper paste. Or peppered and vinegared garlic paste. It tastes great, if consumed in measured amounts. In excessive quantities (>200 g), it starts to be as boring as ten pounds of sauerkraut. In any case, when I was threatened to get bored by garlic and pepper alone, I always had Kimchi.

"We've got ham, eggs, and kimchi, eggs, kimchi, kimchi and ham, kimchi, kimchi, eggs and ham, kimchi...." 😄

Other than that, Korean food has not much to offer. Or that's how it appears to me. Somehow, I was always loaded with garlic. And pepper. 😉

Anyway, coming back home, Karmic Koala aka Ubuntu 9.10 appeared. Since the Mini did great in Korea, I thought it'd deserve an immediate upgrade.

The upgrade went as smooth as upgrades can. Bugs and quirks still present in 9.04 just disappeared. A few comments in the following for completeness.

Karmic comes with an inactive apparmor profile for Firefox. To activate it, issue

sudo aa-enforce /etc/apparmor.d/usr.bin.firefox-3.5

Karmic comes with a cute little firewall called ufw (useless firewall...hey, just kidding 😄 ). In any case, to activate it, type in the following:

sudo -i
ufw enable
ufw logging on
ufw status
ufw allow ssh/tcp (if you want ssh access, for example)

Finally, if you go all the way and encrypt your home partition, you'd probably be sensitive to the way the system logs you in. Karmic shows all user names by default. To change that, issue:

sudo -u gdm gconftool-2 --type bool \
--set /apps/gdm/simple-greeter/disable_user_list 'true'

This way, one still can just login to the user account with no data if asked at immigration. 😉