text: implementing logistic regression from scratch quiz. Initializing Model Parameters¶. We will rewrite the logistic regression equation so that. Descriptive analysis, Pearson's chi-squared test, and multiple logistic regression …. Scikit-learn provide three naive Bayes implementations: Bernoulli, multinomial and Gaussian. The following figures show how by changing the loss function (from hinge-loss to log-loss) in the PEGASOS algorithm, a logistic regression …. Use the family parameter to select between these two algorithms, or leave it unset and Spark will infer the correct variant. As the logistic or sigmoid function used to predict the probabilities between 0 and 1, the logistic regression …. ; h5py is a common package to interact with a dataset that is stored on an H5 file. It can be used in both Binary and Multi-Class …. Before discussing decision trees in depth, let’s go over …. Coursera/Implementing logistic regression from scratch. In our previous Machine Learning From Scratch series, we have covered Linear Regression and Logistic Regression. Follow the steps enlisted below to use WEKA for identifying real values and nominal attributes in the dataset. the actual values from the test dataset. Logistic regression uses the sigmoid function to predict the output. Regression Testing is nothing but a full or partial selection of already executed test …. #Import the required package import torch import torchvision import numpy as np import sys sys. James McCaffrey of Microsoft Research uses a full code program, examples and graphics to explain multi-class logistic regression, an extension technique that allows you to predict a class that can be one of three or more possible values, such as predicting the political leaning of a person (conservative, moderate. Where the right hand side is an odds ratio. We are going to follow the below workflow for implementing the logistic regression model. ) of two classes labeled 0 and 1 representing non-technical and technical article( class 0 is negative class which mean if we get probability less than 0. The main algorithm behind this …. Chapter 14 Logistic Regression Tutorial Logistic regression is one of the most popular machine learning algorithms for binary classification. Today you’ll get your hands dirty by implementing and tweaking the logistic regression algorithm from scratch. Before we implement the multinomial logistic regression in 2 different ways. The curve from the logistic function indicates the likelihood of something such as whether the cells are cancerous or not, a mouse is obese or not based on its weight, etc. Implementing Logistic regression in R programming language with Machinehack's Predict The Data Scientists Salary In following graph depicts the plot between the time a student spends studying versus whether he/she passes or fails the test. For this article, we will use the Cardiovascular Disease dataset from Kaggle. Therefore, just by always predicting class 0, you would get 57% accuracy on the test …. How to Do Multi-Class Logistic Regression Using C#. In logistic Regression, we predict the values of categorical variables. Suppose you are the product manager of the factory and you have the test …. Second, we take the softmax for this row Z i: P i = softmax ( Z i) = e x p ( Z i) ∑ k. scatter_plot_1 Develop the logistic regression model …. Understand the Logistic regression from Scratch. To illustrate the differences between ML and GLS fitting, generate some example data. Logistic regression algorithm can also use to solve the multi-classification problems. Deriving the cost function for Logistic Regression by utilizing the Cross-Entropy function; Implementing the Gradient Descent on Logistic Regression…. So our new loss function (s) would be: Lasso = RSS + λ k ∑ j = 1 | β j | Ridge = RSS + λ k ∑ j = 1β 2j ElasticNet = RSS + λ k ∑ j = 1( | β j | + β 2j) This λ is a constant we use to assign the strength of our regularization. # Splitting the data for training and testing from sklearn. T @ y) If I use the boston housing dataset from scikit learn with this equation my coefficients match what's returned from scikit learn exactly. Logistic Regression — Gradient Descent Optimization — Part 1. I'm having trouble with Polynomial Expansion of features right now. Simple logistic regression. Suppose you want to find the …. Multinomial – Multinomial Logit. We will fit the Logistic regression …. predict(x_test) And voila! You have successfully created a robust, working linear regression …. Refer to the Logistic reg API ref for these parameters and the guide for equations, particularly how penalties are applied. when we have a categorical target variable. Neural networks can seem like a bit of a black box. Machine learning has revolutionized the world of business and is helping us build sophisticated applications to solve tough business problems. The function ‘split_data’ splits the data “Caravan” into test and train (20%) and normalizes it. We suggest a forward stepwise selection procedure. There should be m_train (respectively m_test) columns. , Library for fast text representation and classification. Since we are explaining a logistic regression model the units of the SHAP values will be in the log-odds space. It is one of the simplest classification algorithm in machine learning. Remember, the last entry of this weight vector is the bias coefficient. Here is a histogram of logistic regression trying to predict either user will change a journey date or not. Regularization does NOT improve the performance on the data set that the algorithm used to learn the model parameters (feature weights). Multivariate linear regression…. You are going to be in high demand soon! OpenCV’s latest course offering, Deep Learning With TensorFlow & Keras, has the potential to sweep your career off …. What's our plan for implementing Logistic Regression in NumPy? Let's first think of the underlying math that we want to use. From SVM to Logistic Regression. In this post, I’m going to implement standard logistic regression from scratch. In our case study, we will be working on a churn dataset. I have a very basic question which relates to Python, numpy and multiplication of matrices in the setting of logistic regression. Let's take a closer look into the modifications we need to make to turn a Linear Regression model into a Logistic Regression model. In statistics, logistic regression …. Implementation of Logistic Regression, MLP, CNN, RNN & LSTM from scratch in python. None of the above --------------------------------------------------------------------------------- log likelihood becomes _LESS_ negative, ie: is _INCREASING_ in value. Logistic Regression Using Gradient Descent from Scratch. py, and insert the following code: How to Implement Logistic Regression with Python. Our aim is to classify SMSes in to SPAM or HAM messages using logistic regression and TFIDF vectorizer. , 2008), the authors compared the predic-tive accuracy of regression trees with that of logistic regression models for predicting in-hospital mortality in patients hospitalized with heart failure. The Dickey-Fuller test is a way to determine whether the above process has a unit root. In statistics logistic regression …. Material on generalized linear models and logistic regression, in Chapter 4 and parts of Chapter 5, might also be given emphasis. Logistic Regression is a much more complicated algorithm than Linear regression so we will not implement it from scratch. Handling the unbalanced data using various methods. multiclass logistic regression from scratchdice probability distribution calculator Fairfax County Aau Basketball , Multinomial Logit Model Stata , …. Step-by-step implementation coding samples in Python In this article, we will build a logistic regression model for classifying whether a patient has diabetes or not. Browse The Top 762 Python logistic-regression-for-gender-classification Libraries. g (z) = 1/ (1 + e-z) This is the sigmoid function, or the logistic …. Submissions to the exercises have to be made in Octave or Matlab; in this post I give the solution using R. KNN classifier is one of the simplest but strong supervised machine learning algorithms. , Machine Learning From Scratch…. It is a linear model, just like Linear Regression…. Logistic Regression With Gradient Descent in Excel. The outcome \ (Y\) is either 1 or 0. It helps connect edges in a flow diagram. For example, a correlation of r = 0. Now, let’s load it in a new variable called: data using the pandas method: ‘read_csv’. numpy is the fundamental package for scientific computing with Python. Instead of fitting a straight line or hyperplane, the logistic regression model uses the logistic function to squeeze the output of a linear equation between 0 and 1. So in this article, your are going to implement the logistic regression model in python for the multi-classification problem in 2. , Yes/No), linear regression is not appropriate. 5, then the positive event is true (where x is the predicted probability that the positive event occurs), else the other (negative) event is true. Inventory management II: EOQ extensions, discounts, exchange …. — This post follows the logistic regression post in the “Basics and Beyond” series. Busca trabajos relacionados con Implement logistic regression with l2 regularization using sgd without using sklearn github o contrata en el mercado de freelancing más grande del mundo con más de 21m de trabajos. Here we will present gradient descent logistic regression from scratch …. Logistic regression is a type of generalized linear classification algorithm which follows a beautiful procedure to learn from data. Lasso stands for least absolute shrinkage and selection operator is a penalized regression analysis method that …. Inventory management I: Level demand, EOQ, sensitivity ( PDF ) 8. Logistic Regression could help use predict whether the student passed or failed. Simple logistic regression To test if Grain size is a significant factor, we use the likelihood ratio test. I’ve recently launched Homemade Machine Learning repository that contains examples of popular machine learning algorithms and approaches (like linear/logistic …. This task is intended as a subtask for Measure relative performance of sorting algorithms implementations. We will use the physical attributes of a car to predict its miles per gallon (mpg). In the code below we run a logistic regression …. Cat scratch disease is strongly associated with owning a kitten, and fleas may be involved in its transmission. Logistic Regression is a supervised learning algorithm that is used when the target variable is categorical. The decision boundary can be described by an equation. AutoML is an informal name to a command line tool that can automatically. Implementing logistic regression using numpy in Python and visualizing the objective function variation as a function of iterations. CS282BR - Homework 1- Solution d. We’ll compare our neural net with a logistic regression model and visualize the difference in the decision boundaries produced by these models. Coursera Machine Learning 第三周 quiz Logistic Regression COURSE (9 days ago) Nov 10, 2016 · 本文转载自 mupengfei6688 查看原文 2016-11-10 9844 Andrew Ng/ week3/ Logistic Regression/ log/ machine learning/ mac/ Coursera 1. Step 8: Use the Solver to solve for the regression coefficients. Out of the many classification algorithms available in one's bucket, logistic regression is useful to conduct regression analysis when the target variable (dependent variable) is dichotomous (binary). It validates a candidate's ability to design, implement, deploy, and maintain machine such as linear regression and logistic regression. Here is a recap of the algorithm to implement Logistic Regression, assuming you have a collection of numerical input vectors and the desired true/false output label: Use label smoothing to convert each 0/1 label into 0. Run Logistic Regression With A L1 Penalty With Various Regularization Strengths. At the end we will test our model using training data. For instructions and examples of how to use the logistic regression procedure, see the logistic regression …. Basics of multiple logistic regression. This is why PyTorch offers the " binary cross-entropy with logits " …. Implementing Logistic Regression from Scratch Step by step we will break down the algorithm to understand its inner working and finally will create our own class. Multinomial logistic regression. When we initialize the Support Vector Machine …. In a previous tutorial, we explained the logistic regression …. I've been doing Andrew Ng's excellent Machine Learning course on coursera. We will start from mathematics and gradually implement small chunks into our code. Defining the Softmax Operation¶. Here are the two formulas you will be using: Purpose : Implement the cost function and its gradient for the propagation. The approach used is quite straightforward. To see the value of the intercept and slope calculated by the linear regression algorithm for our dataset, execute the …. Welcome to your first (required) programming assignment! You will build a logistic regression …. Two data samples are matched if they come from repeated observations of the same subject. The Features of both train and test …. We will also see some mathematical formulas and derivations, then a walkthrough through the algorithm's implementation with Python from scratch…. But, if your purpose is to learn a basic machine learning technique, like logistic regression, it is worth it using the core math functions from TensorFlow and implementing it from scratch. Basically, we transform the labels that we have for logistic regression so that they are compliant with the linear regression equations. Common pitfalls in statistical analysis: Logistic regression. Data Science Linear Regression P. As regression problems go, it's actually a fairly complicated algorithm. Given a matrix X we can sum over all elements (by default) or only over elements in the same axis, i. Logistic regression with a neural network mindset simply means that we will be doing a forward and backward propagation mode to code the algorithm as is usually the case with neural network algorithms. Welcome to your first (required) programming assignment! You will build a logistic regression classifier to recognize cats. Logistic Regression is a type of Generalized Linear Model (GLM) that uses a logistic function to model a binary variable based on any kind of independent variables. Machine-Learning-Classification-University-of-Washington / Week2 / week_2_quiz_3_quiz_Implementing logistic regression from scratch. implementing a neural network from scratch in python – an introduction In this post we will implement a simple 3-layer neural network from scratch. Once the Solver is installed, go to the logical regression …. Logistic Regression — ML Glossary documentation. Gradient descent algorithm used to optimize the model parameters (theta) by minimizing the. 11 shows the sigmoidal curve that is fitted by the logistic regression. In this tutorial, you learned the basics of logistic regression and how TensorFlow is used to implement machine learning algorithms. Logistic Regression in Python From Scratch …. First, let's run the cell below to import all the packages that you will need during this assignment. Implement Simple, Multiple, Polynomial Linear Regression [[coding session]] 11. In Multinomial Logistic Regression, you need a separate set of parameters (the pixel weights in your case) for every class. decomposition import PCA from sklearn. Master Machine Learning: Logistic Regression From Scratch With Python. Develop Java games from scratch: 🚨 🚨 🚨 Free Course 🚨 🚨 🚨 🇺🇸 Linear Regression and Logistic Regression using R Studio Functional Skills Math-A self-paced high-quality study Guide- Complete preparation with Worksheets, resources & Quizzes…. Regression using panel data may mitigate omitted variable bias when there is no information on variables that …. In [22]: classifier = LogisticRegression (solver='lbfgs',random_state=0) Once the classifier is created, you will feed your training data into the classifier so that …. This flow diagram is known as the 'Data flow graph'. And that took days (for example, Logistic Regression has no closed form solution, so you need to iteratively solve for the weights/coefficients. We can write the following code: data = pd. We have achieved an accuracy of around 78. Bivariate model has the following structure: (2) y = β 1 x 1 + β 0. Now that our data is well pre-processed, we are ready to build our Logistic Regression model. This time we will be using Logistic Regression. The name “logistic regression” is derived from the concept of the logistic function that it uses. I am confused about the use of matrix dot multiplication versus element wise pultiplication. Logistic Regression Learning Algorithm; # train by Perceptron Learning Algorithm to find best W >>> test_data = 'Each feature of data x separated with spaces. But if you are working on some real project, it’s better to opt for Scikitlearn rather than writing it from scratch …. As announced for the implementation of our regression tree model we will use the UCI bike …. The data is read in as a pandas dataframe, which is very similar to a R dataframe. Machine learning uses statistical concepts to enable machines (computers) to “learn” without explicit programming. Remember, you pick this threshold based on the validation set, then later you'll evaluate it on the test set. Đầu ra dự đoán của logistic regression thường được viết chung dưới dạng: f (x) = θ(wT x) f ( x) = θ ( w T x) Trong đó θ θ được gọi là logistic …. The main conclu-sion is that Logistic regression …. Logistic regression models the data using the sigmoid function. In this tutorial, we will grasp this fundamental concept of what Logistic Regression is and how to think about it. In Chapter 13, we’ll confront another fact: not every …. This is an implementation of a simple logistic regression for binary class labels. After we build the models using training data, we will test the accuracy of the model with test …. Introduction to Binary Logistic Regression 3 Introduction to the mathematics of logistic regression Logistic regression forms this model by creating a new dependent variable, the logit(P). Many software bugs in deep learning come from having matrix/vector dimensions that don't fit. You'll need to have taken the Statistical Thinking and Linear Regression …. We can make this a linear func-tion of x without fear of nonsensical results. When you’re implementing the logistic regression …. The above figure shows a simple linear regression. For logistic regression model given by hypothesis function h (x)=g (Tx)where g is the sigmoid function, if the hypothesis function is h (x)=g (1+2x2+3x3)then the decision boundary is linear. Convert the smoothed labels into the linear domain using the following equation, where y. Regression with binary outcomes Logistic regression coeﬃcients Generalized linear models use link functions, so raw …. 2 suggest a weak, negative association. A few lines of simple algebra will show that its inverse function (also called the “logit” function) is given by. Levels of Service; Consulting; Secret Shopping; HR On Call; logistic regression implementation from scratch. In this example, we would be using the Bank Loan defaulter dataset for modelling through Logistic Regression. This notebook will step you through …. These are useful OLS regression commands for data analysis: lm – Linear Model. Implementing logistic regression from scratch In this section, we will walk through the implementation of logistic regression in Python within the packtml package. This notebook demonstrates, how to build a logistic regression classifier to recognize cats. A good way to see where this article is headed is to take a look at the screenshot of a demo program in Figure 1 and the associated data shown in the graph in Figure 2. The dataset we will be working with is from the marketing department of a bank and has data about whether the customers. We fit a straight line to the data. Before we implement the confusion matrix in Python, we will understand the two main metrics that can be derived from it (aside …. Logistic regression can be binary, helping us to e. An optional, advanced part of this module will cover the derivation of the gradient for logistic regression. Let’s learn how to use scikit-learn to perform Classification and Regression in simple terms. This is intended to give you an instant insight into Logistic-Regression implemented functionality, and help decide if they suit your requirements. Here we will present gradient descent logistic regression from scratch implemented in Python. Regression analysis tries to explain relationships between variables. Let’s talk about a particular algorithm, simple logistic regression, to address the different points using concrete examples. This statement is similar to the CREATE TABLE DDL …. First calculate the first difference, i. Also, we can leave numpy and built a function for calculating dot products. Deep learning consists of composing linearities with non-linearities in clever …. Home; About; Our Team; Services. Logistic Regression is a supervised Machine Learning algorithm, which means the data provided for training is labeled i. We will show a binary classification of two linearly separable datasets. It has 10 classes each representing a digit from 0 to 9. The independent variables can be nominal, ordinal, or of interval type. Ng Computer Science Department Stanford University Stanford, CA 94305 Abstract L1 regularized logistic regression …. The oj * (1 – oj) term is the Calculus derivative of the softmax …. Binomial Logistic Regression (logRegBin) Multinomial Logistic Regression (logRegMulti) Ordinal Logistic Regression (logRegOrd) Frequencies. Get my Free NumPy Handbook:https://www. A number of classification methods were employed in this stage of the process. Example 1: A marketing research firm wants to investigate what factors influence the size of soda (small, …. Assignment 2 - Train Your First Model Lesson 3 - Training Deep Neural Networks on a GPU Assignment 3 - Feed Forward Neural Networks Lesson 4 - Image Classification with Convolutional Neural Networks Lesson 5 - Data Augmentation, Regularization & ResNets Lesson 6: Generative Adversarial Networks and Transfer Learning Project - Train a Deep Learning Model from Scratch. Implementing multiclass logistic regression from scratch Posted: (5 days ago) Nov 08, 2021 · Stack Exchange network consists of 179 …. In Logistic Regression: Example: car purchasing prediction, rain prediction, etc. So, let us try implementing the concept of ROC curve against the Logistic Regression model. Predicting House Prices with Linear Regression. In logistic regression, hypotheses are of interest: The null hypothesis, which is when all the coefficients in the regression …. In this case, they can also be thought as probability of getting 1, \ (p\). Luckily, there’s a tool for everything. 5 from sigmoid function, it is classified as 0. Now, we write the code to implement logistic regression from scratch. 3 Multinomial logistic regression with scikit-learn. We use logistic regression when the dependent variable is categorical. Now, let's take one dataset and implement a logistic regression model from scratch. Machine Learning can be easy and intuitive — here's a complete from-scratch guide to Logistic Regression. If we plot the independent variable (hours) on the x-axis and dependent variable (percentage) on the y-axis, linear regression gives us a …. Logistic Regression is a supervised classification algorithm that uses logistic function to model the dependent variable with discrete possible outcomes. metrics import confusion_matrix from sklearn. Building the Logistic Regression. While using Excel/Google Sheet for solving an actual problem with machine learning algorithms can be a bad idea, implementing the algorithm from scratch with simple formulas and a simple dataset is very helpful to understand how the algorithm works. A sigmoid function is a mathematical function that represents an "s"-shaped curve. This post follows on from linear regression explained. Explore statistical concepts in an interactive way. QUIZ Implementing logistic regression from scratch 8 questions To Pass80% …. As with linear regression, after doing things by hand we will breeze through. For example, prediction of death or survival of patients, which can be coded as 0 and 1, can be predicted by metabolic markers. The simple linear regression model is a line defined by coefficients estimated from training data. Text classification is the automatic process of predicting one or more categories …. Standard linear regression requires the dependent variable to be measured on a continuous (interval or ratio) scale. In this post, you can learn how logistic regression works and how you can easily implement it from scratch using the in python as well as using sklearn. The dependent variable is a binary variable that contains data in the form of either success (1. Step 4: Create the logistic regression in Python. However, this time we'll minimize the logistic loss and compare with scikit-learn's LogisticRegression (we've set C to a large value to disable regularization; more on this in. So we can say logistic regrression is a relationship between the one dependent categorical variable with one or more nominal, ordinal, interval variables. In the new window that pops up, check the box next to Solver Add -In, then click Go. Part 2： Logistic Regression with a Neural Network mindset. We can also check the length of train_set and test_set by using this code. In this free machine learning course, we will be covering the following topics: Python for Data Science. # importing necessary libraries import numpy as np import pandas as pd pd. The tutorial was quite helpful. Artificial Neural Networks (ANN) can be used for a wide variety of tasks, from face recognition to self-driving cars to chatbots! To understand more about ANN in-depth please read this post and watch the below video! ANN can be used for supervised ML regression …. Statistical tests such as regression analysis and t-tests were conducted to test …. I’ve been doing Andrew Ng’s excellent Machine Learning course on coursera. plot logistic regression matplotlibteam curry vs team lebron score. Building a logisitic regression classifier that performs sentiment analysis on tweets can be done in 3 steps: Extract features: process the raw tweets in the training set and extract useful features. The probability of an instance belonging to a certain class is then estimated as the softmax function of the instance's score for that class. A key difference from linear regression …. Some of the key concepts to training most machine learning models have already been covered in my previous article about implementing linear regression from scratch, and most of them can be applied to logistic regression, therefore, they will not be explained in detail again in this article. In the above example, the attribute …. Introduction: Logistic Regression is a supervised learning algorithm that is used when the target variable is categorical. In a previous post, we showed how using vectorization in R can vastly speed up fuzzy matching. Its basic fundamental concepts are also constructive in deep learning. This chapter leverages the following packages. I will explain the process of creating a model right from hypothesis function to algorithm. Winners – February 2022 March 21, 2022. We will be using Pandas for data manipulation, NumPy for array-related work ,and sklearn for our logistic regression model as well as our train-test …. Es gratis registrarse y presentar tus propuestas laborales. 5 Calculate New Coefficients We can. And as a bonus, this course includes both Python and R code templates which you can download and use on your own projects. You will implement your own learning algorithm for logistic regression from scratch, and use it to learn a sentiment analysis classifier. With the likes of sklearn providing an off the shelf implementation of Linear Regression, it is very difficult to gain an insight on what really happens under the hood. · feature_matrix: 2D array of features · sentiment: 1D array of . We took the first two elements from the test set (From Feature Variable)and added a column of ones. Note that this is one of the posts in the series Machine Learning from Scratch. It a statistical model that uses a logistic …. Predicting the age of abalone from physical measurements. In this case we’ll require Pandas, NumPy, and sklearn. The core of the logistic regression is a sigmoid function that returns a value from 0 to 1. See full list on towardsdatascience. We’ll introduce the mathematics of logistic regression …. Then you take the remaining 25% of your data, and test …. Logistic regression from absolute scratch. The hypothesis for logistics regression takes the form of: h θ = g ( z) where, g ( z) is the sigmoid function and where z is of the form: z = θ 0 + θ 1 x 1 + θ 2 x 2. Logistic Regression is a supervised algorithm used to predict a dependent variable that is categorical or discrete. There will be three posts: Linear and logistic regression …. Just as we implemented linear regression from scratch, we believe that multiclass logistic (softmax) regression is similarly fundamental and you ought to know the gory details of how to implement it from scratch. logistic regression from scratch python github, Feb 08, 2020 · Where we used polynomial regression to predict values in a continuous output space, logistic regression is an algorithm for discrete regression…. Tensors are nothing but multidimensional array or a list. “noCIMP” subtype has higher expression of the PDPN gene than the “CIMP” subtype. The sigmoid function and the cross-entropy loss function are meant to be together. (Implement gradient descent from scratch. This tutorial is aimed at implementing Logistic Regression from scratch in python using Numpy. One common way to evaluate the quality of a logistic regression model is to create a confusion matrix, which is a 2×2 table that shows the predicted values from the model vs. As mentioned above, linear regression is a predictive modeling technique. Model Evaluation on Test Data Set. Multinomial regression is used to explain the relationship between one nominal dependent variable and one or more independent variables. From the images given above, it can be clearly seen that the X_train and X_test are well scaled, but we have not scaled Y_train and Y_test as they consist of the categorical data. Logistic Regression is a Machine Learning classification algorithm that is used to predict the probability of a categorical dependent variable. In the above plot, we can see that the cost function . There are some libraries in python to implement KNN, which allows a programmer to make a KNN model easily without using deep ideas of mathematics. Logistic regression is a popular machine learning algorithm for supervised learning – classification problems. Tweets with a positive sentiment have a label of 1, while those with a negative sentiment have a label of 0. The serologic test for rochalimaea may be (odds ratio, 29). Logistic regression should be the first thing to master when becoming a data scientist or a machine learning engineer. [ P ( Y ≤ j) P ( Y > j)] = α j − β X, j ∈ [ 1, J − 1] where j …. The logistic regression model will be approached …. This implementation supports both binary and multi-class classification. Able to write the AdaBoost python code from scratch…. Unconditional logistic regression (Breslow & Day, 1980) refers to the modeling of strata with the use of dummy variables (to express the strata) in a traditional logistic …. Train: Train your logistic regression. Importing Libraries First, let's import the necessary modules. Most machine learning frameworks and toolboxes already provide functions like linear regression and logistic regression, but implementing …. The models that will be introduced in this article are, Logistic Regression; Decision Trees; Random Forest; K nearest neighbor. for the logistic regression cost function, given a xed dataset (of X and y values). In numpy, this can be implemented in the following way: np. txt Go to file Go to file T; Go to line L; Copy path Copy permalink. 2/22/2021 Logistic Regression Tutorial for Machine Learning 6/45 The first training instance is: x1=2. 1 Get and read data batch_size = 256 train_iter, test…. In this first part, we present the dataset we are going to use, the pre-processing involved, the train-test …. You will build a logistic regression classifier to recognize cats. Multiple logistic regression …. In today's tutorial, we are going to cover Logistic Regression from scratch. The only difference is about the probability …. If this is the case, a probability for each categorical variable is produced, with the most probable state being chosen. In this guide, we’ll show a logistic regression example in Python, step-by-step. The vectorized derivative for J is given as: ∇ J ( X) = 1 m X T ( X θ − y) In Python: def compute_gradient(theta, X, y): preds = h(X, theta) gradient = 1/m * X. Linear regression and logistic regression are two of the most popular machine learning models today. Here, our problem is a classification and regression problem. This is not a guide to learn how Logistic regression works (though I quickly explain it) but rather it is a complete reference for how to implement logistic regression …. With this updated second edition, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch…. These include: Logistic Regression…. Logistic Regression establishes a non-linear relationship between the predictors and a binary outcome (0- False & 1-True). Linear regression predictions are continuous (numbers in a range). Logistic Regression From Scratch. case of logistic regression ﬁrst in the next few sections, and then brieﬂy summarize the use of multinomial logistic regression for more than two classes in Section5. Python Statistics From Scratch Machine Learning Itâ s worth bearing in mind that logistic regression is so popular, not because thereâ s some theorem which proves itâ s the model to use, but because it is the simplest and easiest to work with out of a family of equally valid choices. Two main functions in seaborn are used to visualize a linear relationship as determined through regression. Logistic Regression for Machine Learning. It can be used in both Binary and Multi-Class Classification Problems. As each iteration of gradient ascent passes, does the log-likelihood increase or decrease? It increases. The cost function is a summation over the cost for each sample, so the cost function itself must be greater than or equal to zero. Multiclass logistic regression forward path. As the amount of available data, the strength of computing power, and the number of algorithmic improvements continue to rise, so does the importance of data science and machine learning. It is used whenever there is a …. 3 Split the dataset into test …. It was presented at HighLoad++ Siberia conference in 2018. Real-world Example with Python: Now we’ll solve a real-world problem with Logistic Regression. drop ( 'species', axis= 1 ) y = iris [ 'species' ] trainX, testX, trainY, testY = train_test_split (x, y, test…. We need to first grab the last day in the dataframe, and begin assigning each new forecast to a new day. Predictive features are interval (continuous) or categorical. predict (x_test) accuracy = accuracy_score (y_test, pred) print (accuracy) You find that you get an accuracy score of 92. The sigmoid function definition is as follows: When implementing logistic regression, our job is to learn parameters w and b so that ŷ is approximately equal to the test …. In this post I explain how to interpret the standard outputs from logistic regression…. I often present training classes at the company I work for. Multivariate Linear Regression From Scratch With Python. There are many ways to define a loss function and then find the optimal parameters for it, among them, here we will implement in our LogisticRegression class the following 3 ways for learning the parameters:. Figure 1: Classification from a regression/surface-fitting perspective for single-input (left panels) and two-input (right panels) toy datasets. Average item scores for subgroups having the same overall score on the test …. Prerequisites: Understanding Logistic Regression, Logistic Regression using Python. Use your models to solve real-world problems. Today, we will be covering all details about Naive Bayes Algorithm from scratch…. In this section, we show you how to analyze your data using a binomial logistic regression in Stata when the six assumptions in the previous section, Assumptions, have not been violated. SUBSCRIBE with NOTIFICATIONS ON 🔔 if you enjoyed the video!#GregHogg #DataScience #MachineLearningFollow me on LinkedIn: …. We will use a simple dummy dataset for …. KNN is a Supervised algorithm that can be used for both classification and regression tasks. Training a linear regression model using the gradient descent algorithm; Implementing gradient descent and linear regression using PyTorch built-in. Rest Logistic Regression. How To Implement Logistic Regression From Scratch in Python. If you haven’t already install the Solver in Excel, use the following steps to do so: Click File. 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Step 3: Import ‘KNeighborsClassifier’ class from Sklearn. Now that we know what we have to optimize, let’s apply it and code our logistic regression in R from scratch. So, based on a set of independent variables, logistic regression …. Logistic regression is the simplest classification algorithm you'll ever encounter. Interpretation • Logistic Regression • Log odds • Interpretation: Among BA earners, having a parent whose highest degree is a BA degree versus a 2-year …. We will start off with a brief recap of what logistic regression seeks to accomplish and then go over the source code and look at an example. Machine learning: linear regression Linear regression. We will start from Linear Regression and use the same concept to build a 2-Layer Neural Network. Nowadays, it’s commonly used only for constructing a baseline model. Most questions will be true/false or multiple choice, with perhaps 1-3 short answer questions. After this, our training (and test) dataset is a numpy-array where each column represents a flattened image. Spring Boot is a widely used Java framework that makes it easy to create stand-alone Spring-based applications. ; PIL and scipy are used here to test …. Logistic Regression is a linear …. This assignment will step you …. Now, set the independent variables (represented as X) and the dependent variable (represented as y): X = df [ ['gmat', 'gpa','work_experience']] y = df ['admitted'] Then, apply train_test_split. Logistic Regression on Digit Recognition. If the “regression” part sounds familiar, yes, that is because logistic regression is a close cousin of linear regression—both. Today you'll get your hands dirty by implementing and tweaking the logistic regression algorithm from scratch. In linear regression, we find the best fit line, by which we can easily predict the output. In the last article, you learned about the history and theory behind a linear regression machine learning algorithm. Finally we shall test the performance of our model against actual Algorithm by scikit learn. Step 4: Create the Model in Python (In this example Logistic Regression) Step 5: Predict using Test …. However, to test the code, we will switch our attention to logistic regression …. Splitting X and y into training and testing sets. implementing logistic regression from scratch python; implementation of logistic regression model; logit model in python; the command to predict the logistic regression model ‘model’ on test dataset (test) is: how to generalise logistic regression python; logistic regression …. logistic regression implementation from scratch. As in linear regression, the logistic regression …. We will only use the linear algebra tools available in R. 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PCA AND LDA (MACHINE LEARNING) Akhilesh Joshi [email protected] When we plot these datasets it looks like this. model_selection module and fitting a logistic regression model using the statsmodels package/library. Modelling Binary Logistic Regression Using Python. You will pass to fminunc the following inputs: • The initial values of the parameters we are trying to optimize.


text:
# Math Help - Laplace Transform Gamma Function

1. ## Laplace Transform Gamma Function

I am just looking for a proof or help to solve the Laplace Transform that:

f(t^α) = [ Γ(α+1) ] / [ s^(α+1) ]

I dont even know where to begin working on this and any help would be greatly appreciated.
Thanks.

2. You need the definition of the Laplace transform and make a substitution as follows:
$\int_0^{+\infty}e^{-st}t^a dt$
Now set:
$st=u \qquad s>0$
You can rewrite this after the substitution as:
$\frac{1}{s^{a+1}}\int_0^{+\infty}e^{-u}u^a du$
Which can be written using the definition of the Gamma function to the required result.

3. I'm not seeing how substituting in u for st is turning the t into a u.

4. Originally Posted by eeverett1
I'm not seeing how substituting in u for st is turning the t into a u.
$\int_0^{\infty} e^{-st}t^a dt = \int_0^{\infty} e^{-st} \left( \frac{st}{s} \right)^a dt = \frac{1}{s^a}\int_0^{\infty} e^{-st}(st)^a dt$.
Now let $\mu = st$ so then $\frac{1}{s^{a+1}} \int_0^{\infty} e^{-\mu} \mu^a d\mu$.

format: plain


text:
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# In the figure above, is the area of triangular region ABC

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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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24 Aug 2013, 03:55
mau5 wrote:
leroyconje wrote:
WAIT WAIT WAIT....

in my opinion statement 1) is sufficient.

AC is less than AD, and BC must be less than AB (leg vs hypotenuse) therefore Area cannot be equal. 1) sufficient.

choice A is correct?

Refer to the posts above, AC>AD.

MY GOOD what a distraction!
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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18 Sep 2013, 17:14
EvaJager wrote:
jfk wrote:
Attachment:
OG13DS79v2.png
In the figure above, is the area of triangular region ABC equal to the area of triangular region DBA ?

(2) ∆ABC is isosceles.

Source: OG13 DS79

The area of a right triangle can be easily expressed as half the product of the two legs.
Area of triangle $$ABC$$ is $$0.5AC\cdot{BC}$$ and that of the triangle $$DBA$$ is $$0.5AD\cdot{AB}$$.

The question in fact is "Is $$AC\cdot{BC} = AB\cdot{AD}$$?"

(1) From $$AC^2=2AD^2$$, we deduce that $$AC=\sqrt{2}AD$$, which, if we plug into $$AC\cdot{BC} = AB\cdot{AD}$$, we get $$\sqrt{2}AD\cdot{BC}=AB\cdot{AD}$$, from which $$\sqrt{2}BC=AB$$. This means that triangle $$ABC$$ should necessarily be isosceles, which we don't know.
Not sufficient.

(2) Obviously not sufficient, we don't know anything about $$AD$$.

(1) and (2): If $$AC=BC=x$$, then $$AB=x\sqrt{2}$$, and $$AD=\frac{x}{\sqrt{2}}$$.
Then $$AC\cdot{BC}=AB\cdot{AD}=x^2$$.
Sufficient.

I'm a little confused with this method.

1) In statement 1, how can you deduce that the ABC needs to be an isosceles?
2) When you combine the statements, How do you know that $$AD=\frac{x}{\sqrt{2}}$$?
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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18 Nov 2013, 21:37
teal wrote:
does anyone have any other alternative method to solve?

Don't use numbers, use logic.

Vandygrad above helped me break this down. Look up what an Isosceles triangle is: Which is a triangle that has 2 equal sides, and 2 equal angles, so with that information on hand, you know that it's a 45/45/90 , and look up how to find the area of a triangle A=Base*Height/2, or A=1/2(B*H).

The question stem states that the area of ABC and DBA, is it the same? Yes/No?

1) No values are given for ABC/or or DBA. INSUF.

So you have an equation for C, but no know lengths, so insufficient to solve for the area. Knowing the formula is irrelevant, values are important. Time Saver.

2) ABC=Isocolecs: so you know the triangle has 2 equal sides, and 2 equal angels. No lengths, to be able to determine the area of triangle ABC:

Combined) C is solved for. Given: *****ABC = Isocolesces, you have two equal sides, that and knowing that you can reduce statement 1, then use the P. Theorem to solve: Stop here. Sufficient to solve.
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07 Aug 2014, 02:04
EvaJager wrote:
jfk wrote:
Attachment:
OG13DS79v2.png
In the figure above, is the area of triangular region ABC equal to the area of triangular region DBA ?

(1) and (2): If $$AC=BC=x$$, then $$AB=x\sqrt{2}$$, and $$AD=\frac{x}{\sqrt{2}}$$.
Then $$AC\cdot{BC}=AB\cdot{AD}=x^2$$.
Sufficient.

Can anyone explane the last step? AC * BC = AB * AD = x^2 ?

x * x = x√2 * x/√2

x^2 = x^2*√2/√2 ---> is this right to solve the equation like this?
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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12 Mar 2015, 08:58
I understand the mathematical/algebraic approach, but is it possible to answer this question using logic alone?

For example:

Statement 1 fixes the ratio of AC to AD, but point B is still free to move in space, so insufficient.
Statement 2 fixes the ratio of AC to BC, but point D is still free to move in space, so insufficient.

Together, the ratio of all the sides are fixed, so sufficient.

Does the above approach make sense?
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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12 Mar 2015, 19:53
swaggerer wrote:
I understand the mathematical/algebraic approach, but is it possible to answer this question using logic alone?

For example:

Statement 1 fixes the ratio of AC to AD, but point B is still free to move in space, so insufficient.
Statement 2 fixes the ratio of AC to BC, but point D is still free to move in space, so insufficient.

Together, the ratio of all the sides are fixed, so sufficient.

Does the above approach make sense?

The two statements are fine but you need to think through the "using both" part clearly. I have discussed the logical approach here: in-the-figure-above-is-the-area-of-triangular-region-abc-134270.html#p1134780
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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13 Apr 2015, 18:45
Hi erikvm,

Yes, TESTing VALUES on this question is a great way to deal with a situation that is really 'technical.' As long as you're labeling your work and being thorough, you'll find that this approach works on LOTS of Quant questions.

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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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14 Apr 2015, 22:35
Hi erikvm,

TESTing VALUES is a useful approach on most DS questions; you just have to be sure to adjust the tactic a bit. On a PS question, you're (typically) looking for the one answer that matches your values. On a DS question, you're TESTing multiple VALUES to see if a pattern emerges (or if you can prove that a pattern does NOT exist). Since that strategy works in so many different ways on Test Day, it's a great approach to practice throughout your studies.

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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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11 May 2015, 00:07
jfk wrote:
Attachment:
OG13DS79v2.png
In the figure above, is the area of triangular region ABC equal to the area of triangular region DBA ?

(2) ∆ABC is isosceles.

Source: OG13 DS79

Ans C.

Keep CB as x. From equation 1, we get (AC)^2=2(AD)^2 , which gives as AD = x/ root 2. - NS

From 2, we get both AC and CB are x. which implies AB is root 2 * x. - NS as no info about other triangle.

Combine. we can find the area of both the triangles and its equal. Keeping CB as x is the key here. Hope it helps
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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20 Jul 2015, 21:19
ltkenny wrote:
I still don't get it.
To compare the Area of (ABC) and Area of (DBA):
Then look at the graph:
(AB) is the hypotenuse of triangle (ABC)
-> AB > CB (2)
(1) and (2) :
-> the answer is NO, their areas are not equal
Thus, the answer must be A.
Can anyone please explain my mistake in here? Thanks

I got the same answer first. Then, i thought,
AB^2=AC^2+BC^2
That means Area of triangle ABD is
=0.5*sqrt(AC^2+BC^2)*AC/sqrt(2) which maybe greater than 0.5*AC*BC .
Unless you know BC and Ac values, you cannot say if area is greater, because of the square root 2, you cannot say, it reduces the value to 0.707 of the value.
So, it may be or may not be greater. Hence, it's not A.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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28 Jul 2015, 22:04
My approach on this was:

Is Area ABC = Area DBA ?

Area ABC = (CB.AC)/2

So, we are reduced to: Is (CB.AC)/2 = (AB.AD)/2 ? even further: Is (CB.AC)= (AB.AD) ?

St1-
√2(CB)= (AB) ? Cannot affirm anything about it ---> NOT SUFF

St2-
Triangle ABC is isoceles, so (AC)=(CB), but nothing can be affirmed the other segments: (AB) and (AD) ---> NOT SUFF

St1/2-
We know until now:
√2(CB)= (AB)
(AC)=(CB)
(AC)^2 + (CB)^2 = (AB)^2 (Pythagorean Theorem)

(CB)^2 + (CB)^2 = (AB)^2
2(CB)^2 = (AB)^2
√2(CB)=(AB)

Going back on the first equation:
yes, the areas are equal

I think I could've stopped in that moment where I noticed with all the three equations in hand I could find the relation between the areas.

Does this make sense ?
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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16 Feb 2016, 20:17
took me some time to solve it..
we know that both triangles are right angles.
we are asked for areas if are equal
area is bxh/2

AC*CB=AD*AB - this is our question.

we know that:
AC^2+CB^2=AB^2

doesn't tell much.

2. ABC is isosceles. AC=CB
ok, so AB^2=2AC^2 or AB=AC*sqrt(2)

area of ABC is AC^2/2

area of ABD is AB*AD/2. we know AB, but it doesn't help much, as we still have 2 unknowns - AC and AD.

1+2.

since we found out in 2 that we have 2 unknowns, 1 fills out the gap:

We know that AB^2=2AC^2. we also know that AC^2=2AD^2.

we see that the areas are equal.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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08 Mar 2016, 07:49

triangle ABC area = AC*BC/2 AND TRinagle ADB area = AD*AB/2= ROOT2 AC* AB/2

SO Triangle ADB area will be always greater than triangle ABC REASON AB is the diagonal of right angle triangle abc and AB will be always greater than BC
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08 Mar 2016, 07:57
vijaisingh2001 wrote:

triangle ABC area = AC*BC/2 AND TRinagle ADB area = AD*AB/2= ROOT2 AC* AB/2

SO Triangle ADB area will be always greater than triangle ABC REASON AB is the diagonal of right angle triangle abc and AB will be always greater than BC

Follow posting guidelines (link in my signatures). Search for a question before you post, type in the complete question and do not use pictures for questions. Topics merged.

The list of OG2013 quant questions is at the-official-guide-quantitative-question-directory-143450.html

Do not waste your time in questioning the answers of the official guide. They are always correct.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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08 Mar 2016, 08:07
vijaisingh2001 wrote:

triangle ABC area = AC*BC/2 AND TRinagle ADB area = AD*AB/2= ROOT2 AC* AB/2

SO Triangle ADB area will be always greater than triangle ABC REASON AB is the diagonal of right angle triangle abc and AB will be always greater than BC

C is the correct answer for this question.

Your statement above is NOT correct.

Area (ABC) = 0.5*AC*AB = 0.5*$$\sqrt{2}$$*AD*BC = 0.7 * AD*BC

Now although, BC < AB , do you know for sure that 0.7*BC = (a fixed value)* AB , do you know the 'fixed value'? NO. This the reason why this statement is NOT sufficient. Be careful with your interpretations in DS questions. You must be absolutely sure of the final value.

Hope this helps.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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22 Jun 2016, 22:09
Area (ABC) = 1/2*AC*BC
Area (DBA) = 1/2*DA*AB

Statement 1:
AC = √2* AD. But we do not know anything about the base
ISUFFICIENT

Statement 2:
We just have the information about ABC
INSUFFICIENT

Combining both statements:
On combining, AC = CB, and AC = √2*AD

We have the values of base and perpendicular of both triangles in terms of AD.
Hence we can calculate and compare the area
SUFFICIENT

Correct Option: C
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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01 Dec 2016, 03:50
My approach on this one was as follows:

I reworded the question, so if the question asks if the area of triangular region ABC is equal to the area of triangular region DBA, then it means that

$$( (AC) (CB) ) / 2 = ((AD) (AB)) /2$$, we can simplify it as $$(AC) (CB) = (AD) (AB)$$. The reworded question is then $$(AC) (CB) = (AD) (AB)$$ ?

1) $$(AC)^2 = 2(AD)^2$$

$$\sqrt[2]{(AC)^2}= \sqrt[2]{2(AD)^2}$$

$$AC = AD \sqrt[2]{2}$$

But we don't know anything about CB and AB so the stem is Insufficient.

2) ABC is isosceles.

We don't know anything about the measures of each triangle so, stem (2) is insufficient.

Together (1) and (2):

We know that the proportions between AC and AD from stem 1. That's to say,
$$AC = AD \sqrt[2]{2}$$

And we know that an isosceles triangle has two of the sides that are equal and they always follow this proportion: $$x:x:x\sqrt[2]{2}.$$

So AC and CB should be equal. That means, $$CB = AD \sqrt[2]{2}$$
and if $$x = AD \sqrt[2]{2}$$ then $$AB = AD \sqrt[2]{2} \sqrt[2]{2} = AD \sqrt[2]{4} = 2(AD)$$

Then area of ACB is $$((AD \sqrt[2]{2}) (AD \sqrt[2]{2}) ) / 2 = (2(AD)^2)/2$$
And area of DAB is $$((AD) 2(AD))/2 = (2(AD)^2)/2$$

That means, $$(2(AD)^2)/2 = (2(AD)^2)/2$$ so area of ACB and area of DAB are equal.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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29 May 2017, 19:02
I think I found an effective way of solving this problem in under two minutes. Let me explain the logic of it:

For simplicity purposes, let's call $$(\overline{AC})=x; (\overline{CB})=y; (\overline{AD})=w$$; and $$(\overline{AB})=z$$.

The question is basically asking if $$xy=wz$$.

Let's analyze the statements:

Statement 1)

$$x^{2}=2w^{2}$$. You can solve for $$w$$ and see that $$w=\frac{x\sqrt{2}}{2}$$. This does not help us to answer the question, so Statement 1 is not sufficient.

Statement 2)

∆ABC being an isosceles right triangle means that the triangle is a $$x:x:x\sqrt{2}$$ triangle. In other words, that $$x=y$$, and consequently that $$\text{A}^{ABC}=\frac{x^{2}}{2} \rightarrow 2\text{A}^{ABC}=x^{2}$$. Again, useful, but not sufficient.

Statements 1 and 2)

From Statement 2 we know that $$2\text{A}^{ABC}=x^{2}$$, and from Statement 1 we know that $$x^{2}=2w^{2}$$. From these, we can say that:

$$2\text{A}^{ABC}=2w^{2} \rightarrow \text{A}^{ABC}=w^{2} \rightarrow \frac{xy}{2}=w^{2}$$. It's time to use some of the information we had from Statement 1, in this case regarding $$w$$:

$$\frac{xy}{2}=\left(\frac{x\sqrt{2}}{2}\right)^{2} \rightarrow \frac{xy}{2}=\frac{x^{2}}{2}$$.

Now, since from Statement 2 we know that $$x=y$$, then the equation will hold true, and therefore, the correct answer is C.

Hope it helps.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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06 Jul 2017, 10:32
Area of triangle ABC= 1/2 * AC*CB

This just gives a relation between AC and AD. We can't estimate exact values.

2) AC=CB
Therefore it is a 45-45-90 triangle with sides in ratio 1:1: sq.root 2

Now our question becomes: Is AC^2= AD*AB

No information about any other side.

Both
We can say that:

Area of ABC= x^2/2
Area of DAB= x^2/2

The area of both the triangles is same.
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Re: In the figure above, is the area of triangular region ABC  [#permalink]

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29 Apr 2018, 02:24
Hi the question is
is the area of triangular region ABC equal to the area of triangular region DBA ?

from Statement 1 we know
Which means AC is probably bigger than AD . however for the area of a triangle we need the relation to both Height and Base to draw a conclusion hence insufficient.
From Statement 2 we know

(2) ∆ABC is isosceles.
However we still have no idea about AD HENCE WE STILL CONT COMPARE AREAS OF BOTH THE TRIANGLES.

Now together we know
(2) ∆ABC is isosceles.

Using both, ratio of sides of ABC are 1:1:2 √
1:1:2
= AC:BC : AB
Area of ABC = 1/2*1*1 = 1/2

Area of DAB = 1/2∗AD∗AB=1/2∗1/2 √ ∗2 √ =1/2

Areas of both the triangles is the same
Re: In the figure above, is the area of triangular region ABC   [#permalink] 29 Apr 2018, 02:24

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# Write in the Form 'Nth Root of A' in the Following Number. 100 1 19 - SSC (English Medium) Class 8 - Mathematics

ConceptMeaning of Numbers with Rational Indices

#### Question

Write in the form 'nth root of a' in the following number.

100^(1/19)

#### Solution

100^(1/19)

= Nineteenth root of 100

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 3: Indices and Cube root
Practice Set 3.1 | Q: 2.5 | Page no. 15
Solution Write in the Form 'Nth Root of A' in the Following Number. 100 1 19 Concept: Meaning of Numbers with Rational Indices.
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## Constructive gem: an injection from Baire space to natural numbers

I am not sure whether to call this one a constructive gem or stone. I suppose it is a matter of personal taste. I think it is a gem, albeit a very unusual one: there is a topos in which $\mathbb{N}^\mathbb{N}$ can be embedded into $\mathbb{N}$. Continue reading Constructive gem: an injection from Baire space to natural numbers

## Constructive gem: double exponentials

In the last constructive gem we studied the exponential $2^\mathbb{N}$ and its isomorphic copies. This time we shall compute the double exponential $2^{2^\mathbb{N}}$ and even write some Haskell code. Continue reading Constructive gem: double exponentials

## Constructive gem: juggling exponentials

Constructive gems are usually not about particular results, because all constructive results can be proved classically as well, but rather about the method and the way of thinking. I demonstrate a constructive proof which can be reused in three different settings (set theory, topology, computability) because constructive mathematics has many different interpretations.

## Constructive stone: minima of sets of natural numbers

I promise I will post a constructive gem soon. This constructive stone came up as a reaction to the cardinality of finite sets stone. I show that inhabited sets of natural numbers need not have minima, constructively.

## Constructive stone: cardinality of sets

Cardinality of sets in constructive mathematics is not as well behaved as in classical mathematics. Cardinalities of finite sets are not natural numbers, and cardinalities are not linearly ordered.

## Constructive stone: finite sets

Just like in real life, constructive stones are easier to find than constructive gems, so let me start the series with a stone about constructive finite sets.

Two girl one cup

Continue reading Constructive stone: finite sets

## Constructive gems and stones

In various mathematical forums, mostly those of a logical flavor, I regularly see people asking basic questions about constructive mathematics. I also see misconceptions about constructive mathematics. I shall make a series of posts, Constructive Gems and Stones, which will answer basic questions about constructive mathematics, and will hopefully help fix wrong ideas about constructive mathematics.

A [...]


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Home > Standard Error > Linear Regression And Standard Error

# Linear Regression And Standard Error

## Contents

R-squared will be zero in this case, because the mean model does not explain any of the variance in the dependent variable: it merely measures it. An Error Occurred Unable to complete the action because of changes made to the page. For example: x y ¯ = 1 n ∑ i = 1 n x i y i . {\displaystyle {\overline ∑ 2}={\frac ∑ 1 ∑ 0}\sum _ − 9^ − 8x_ The latter case is justified by the central limit theorem. click site

That's it! e) - Διάρκεια: 15:00. Is there a word for spear-like? You can choose your own, or just report the standard error along with the point forecast. http://onlinestatbook.com/lms/regression/accuracy.html

## Standard Error Of The Slope

In a simple regression model, the percentage of variance "explained" by the model, which is called R-squared, is the square of the correlation between Y and X. The least-squares estimate of the slope coefficient (b1) is equal to the correlation times the ratio of the standard deviation of Y to the standard deviation of X: The ratio of Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the How To Calculate Standard Error Of Regression Coefficient Matt Kermode 257.656 προβολές 6:14 Simplest Explanation of the Standard Errors of Regression Coefficients - Statistics Help - Διάρκεια: 4:07.

For large values of n, there isn′t much difference. Star Strider Star Strider (view profile) 0 questions 6,544 answers 3,168 accepted answers Reputation: 17,038 on 21 Jul 2014 Direct link to this comment: https://www.mathworks.com/matlabcentral/answers/142664#comment_226685 My pleasure! In other words, α (the y-intercept) and β (the slope) solve the following minimization problem: Find  min α , β Q ( α , β ) , for  Q ( α Read More Here The error that the mean model makes for observation t is therefore the deviation of Y from its historical average value: The standard error of the model, denoted by s, is

Thanks for the question! Standard Error Of Estimate Interpretation Standard Error of Regression Slope was last modified: July 6th, 2016 by Andale By Andale | November 11, 2013 | Linear Regression / Regression Analysis | 3 Comments | ← Regression Join the conversation ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection to 0.0.0.10 failed. Is the R-squared high enough to achieve this level of precision?

## Standard Error Of Regression Formula

Although the OLS article argues that it would be more appropriate to run a quadratic regression for this data, the simple linear regression model is applied here instead. http://www.statisticshowto.com/find-standard-error-regression-slope/ fitlm gives you standard errors, tstats and goodness of fit statistics right out of the box:http://www.mathworks.com/help/stats/fitlm.htmlIf you want to code it up yourself, its 5 or so lines of code, but Standard Error Of The Slope S is 3.53399, which tells us that the average distance of the data points from the fitted line is about 3.5% body fat. Standard Error Of The Regression For example, type L1 and L2 if you entered your data into list L1 and list L2 in Step 1.

However, those formulas don't tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\hat {\alpha }}} and β ^ {\displaystyle {\hat {\beta }}} vary from get redirected here Red balls and Rings How do spaceship-mounted railguns not destroy the ships firing them? Your cache administrator is webmaster. X Y Y' Y-Y' (Y-Y')2 1.00 1.00 1.210 -0.210 0.044 2.00 2.00 1.635 0.365 0.133 3.00 1.30 2.060 -0.760 0.578 4.00 3.75 2.485 1.265 1.600 5.00 Standard Error Of Regression Coefficient

Browse other questions tagged standard-error inferential-statistics or ask your own question. is a privately owned company headquartered in State College, Pennsylvania, with subsidiaries in the United Kingdom, France, and Australia. statisticsfun 138.149 προβολές 8:57 How to Calculate R Squared Using Regression Analysis - Διάρκεια: 7:41. navigate to this website In the mean model, the standard error of the mean is a constant, while in a regression model it depends on the value of the independent variable at which the forecast

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## For example, the standard error of the estimated slope is $$\sqrt{\widehat{\textrm{Var}}(\hat{b})} = \sqrt{[\hat{\sigma}^2 (\mathbf{X}^{\prime} \mathbf{X})^{-1}]_{22}} = \sqrt{\frac{n \hat{\sigma}^2}{n\sum x_i^2 - (\sum x_i)^2}}.$$ > num <- n * anova(mod)[[3]][2] > denom <-

Return to top of page. mathwithmrbarnes 320.734 προβολές 9:03 Standard Error - Διάρκεια: 7:05. Was there something more specific you were wondering about? Standard Error Of Estimate Calculator Andale Post authorApril 2, 2016 at 11:31 am You're right!

The standard error of the forecast gets smaller as the sample size is increased, but only up to a point. Also, the estimated height of the regression line for a given value of X has its own standard error, which is called the standard error of the mean at X. The coefficients, standard errors, and forecasts for this model are obtained as follows. my review here asked 2 years ago viewed 17999 times active 1 year ago Get the weekly newsletter!

That's too many! I would really appreciate your thoughts and insights. It is also possible to evaluate the properties under other assumptions, such as inhomogeneity, but this is discussed elsewhere.[clarification needed] Unbiasedness The estimators α ^ {\displaystyle {\hat {\alpha }}} and β Suppose our requirement is that the predictions must be within +/- 5% of the actual value.

The correlation between Y and X , denoted by rXY, is equal to the average product of their standardized values, i.e., the average of {the number of standard deviations by which By using this site, you agree to the Terms of Use and Privacy Policy. For example, if γ = 0.05 then the confidence level is 95%. Can you show step by step why $\hat{\sigma}^2 = \frac{1}{n-2} \sum_i \hat{\epsilon}_i^2$ ?

When one independent variable is used in a regression, it is called a simple regression;(...) ^ Lane, David M. I could not use this graph. Please help. Applied Regression Analysis: How to Present and Use the Results to Avoid Costly Mistakes, part 2 Regression Analysis Tutorial and Examples Comments Name: Mukundraj • Thursday, April 3, 2014 How to

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# Independence of Axioms in an axiomatic system

How do we show that we are using independent axioms in an axiomatic systems i.e

1. $A\rightarrow (B \rightarrow A)$

2. $(A\rightarrow (B\rightarrow C)) \rightarrow ((A\rightarrow B)\rightarrow (A\rightarrow C))$

3. $(\lnot A\rightarrow \lnot B)\rightarrow (B\rightarrow A)$

I think I know how to show that the third is independent of the first two, we can take $\lnot \phi = \phi$ and then the first two are still valid but the third is not, but I'm not sure how to go about doing this for the other axioms.

Thanks for any help.

-
(1) is certainly independent of the others, since it is false (with the standard interpreations of the symbols) while the others are true. –  Chris Eagle Feb 21 '12 at 23:45
Ah sorry I had the axiom wrong! –  hmmmm Feb 21 '12 at 23:48
As usual in logic, independence is proven by constructing a suitable model. For example, what if we interpret $\to$ as "iff"? –  Zhen Lin Feb 22 '12 at 7:25
@hmmmm: In your comment, by "the second axiom", did you mean the third? –  joriki Feb 22 '12 at 16:34
People don't get notified of your comments unless you ping them using the @username idiom. Yes, that's correct -- so that shows that the other two are independent of that one taken alone, not the other way around as you said in your previous comment. –  joriki Feb 22 '12 at 17:23

OK so here goes,

To show that these three axioms are all independent we want to construct an interpretation that shows that two of the axioms are still valid but the third is not (as said in the comments). The first of these will just use two truth values (T,F) and the rest will use three (T,F,A).

To show that A3) is independent from A1) and A2)

This is the simplest case, we simply let our interpretation of $\lnot\phi$ and $\phi$ be the same. In this case we can see that A3) is no longer valid, by taking $A=F$ and $B=T$ then this is no longer valid but A1) and A2) obviously still are (they don't have a negation in them).

To show that A2) is independent from A1) and A3)

$\begin{array} \hline A & B & A\rightarrow B \\ \hline T & T & T \\ \hline T & A & A \\ \hline T & F & F \\ \hline A & T & T \\ \hline A & A & T \\ \hline A & F & A \\ \hline F & T & T \\ \hline F & A & T \\ \hline F & F & T \\ \hline \end{array}$

$\begin{array} \hline A & \lnot A \\ \hline T & F \\ \hline A & A \\ \hline F & T \\ \hline \end{array}$

We can now see that under these new interpretations that A1) and A3) are still valid but A2) is no longer valid under this new interpretation.

Showing that A1) is independent from A2) and A3)

We use the same argument as above but with the first table slightly different:

$\begin{array} \hline A & B & A\rightarrow B \\ \hline T & T & T \\ \hline T & A & F \\ \hline T & F & F \\ \hline A & T & T \\ \hline A & A & T \\ \hline A & F & F \\ \hline F & T & T \\ \hline F & A & T \\ \hline F & F & T \\ \hline \end{array}$

$\begin{array} \hline A & \lnot A \\ \hline T & F \\ \hline A & A \\ \hline F & T \\ \hline \end{array}$

So we can see that A1) is independent from A2) and A3) as they are still valid here but A1) is not.

We have now shown that these three axioms are independent from each other. (We should also notice that modus ponens is preserved under these two new interpretations)

-
This sort of independence proof implies a bounded lattice of logical systems, if we take the empty axiom set under modus ponendo ponens as a rule of inference as a logical system also. Presuming the rule of inference understood, the atoms of this lattice are the individual axioms. Their join is simply their union, and the meet is simply the intersection of the axiom sets. –  Doug Spoonwood Jun 21 '13 at 1:19
The first truth table here for "→" and "¬" has the same semantics as Lukasiewicz's three-valued logic. –  Doug Spoonwood Jun 21 '13 at 1:28


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# Computing two-electron integrals with an STO-3G basis set

I am trying to implement a restricted Hartree-Fock calculation using an STO-3G basis set, for fun. I managed to perform this calculation where only $\mathrm{1s}$ orbitals are present ($\ce{H2}$ and $\ce{HeH+}$) as explained in Szabo and Ostlund's book. In this book, authors give explicit formulas for overlap, kinetic, nuclear-electron, and electron-electron integrals for $\mathrm{1s}$ orbitals and they work correctly.

In order to generalize my calculation to systems containing $\mathrm{2s}$ and $\mathrm{2p}$ orbitals (for $\ce{H2O}$ and $\ce{N2}$), I used the general formulas I found in Cook's book for the electron-nuclear and electron-electron integrals. In this case, I obtain results that are slightly different from Szabo's book:

$$E_\text{tot}(\ce{H2O}) = -74.4442002765 \text{ a.u.}$$

$$E_\text{tot}^\text{Szabo}(\ce{H2O}) = -74.963 \text{ a.u.}$$

This is obviously problematic since orbital energies suffer from the same error and this leads to an erroneous ionization potential (0.49289045 a.u. instead of 0.391 a.u., a difference of approximately 63 kcal$\cdot$mol$^{-1}$).

Since I checked my code multiple times and I wrote the two-electron computation code from scratch twice, I was wondering if there is a typo in Cook's book. Is there is a good reference where I can find the (correct) formula to compute two-electron integrals of gaussian functions (in Cartesian coordinates) with arbitrary angular momenta? At the moment I am not looking for a very efficient (recursive) algorithm to perform this task, I only need an exact formula like the one proposed in Cook's book.

Sources:

[1] Szabo and Ostlund, Modern Quantum Chemistry, Dover, 1989.

[2] Cook, Handbook of Computational Chemistry, Oxford University Press, 1998.

• Can you put your code on github? Difficult to answer the question without seeing your formulae. Your result could be due to a floating point error ... I've found this when reproducing the computations of other scientists. – user1945827 Nov 19 '15 at 6:37
• @user1945827 I was thinking about the same thing, but many calculations (see Geoff's answer) gives a value of -74.96(...). My code is already on GitHub (github.com/RMeli/Hartree-Fock) but I didn't gave the link because I didn't wanted too much help! ;) The routine computing the integrals is the ELECTRONIC in INTEGRALS.PY (the program is in Python because I can code fast, but I will migrate it to fortran when it works fine). – user23061 Nov 19 '15 at 9:04
• consider scholar.google.ru/… – permeakra Nov 19 '15 at 14:32
• @permeakra I spent much time using Google and Google Scholar. However, Google Scholar results are normally about very efficient algorithms to compute two-electron integrals. What I would like to implement at first is an exact formula (like the one proposed in Cook's book or in Szabo's book for 1s orbitals). – user23061 Nov 19 '15 at 14:41
• @R.M. This article is on the first page of the google scholar link from above.... I dunno, seems suspiciously like what your want. rspa.royalsocietypublishing.org/content/royprsa/258/1294/… – permeakra Nov 19 '15 at 15:33

Actually there is a mistake in the analtical expression in Cook's Book. On his web page he has a pdf with the corrected verison

http://spider.shef.ac.uk/

Maybe this solves your problem, but I would also recommend to implement the Obara-Saika Scheme or rys-Quadrature since they are really much more efficient. If your are programming in Python, you might have a look at the PyQuante project, which implements all this stuff. Concerning Obara-Saika you might also read about the Head-Gordon Pople Scheme. It is in principial an adapted version of Obara-Saika which reduces the FLOP count.

• This DO solve my problem!!! Thank you!!! I will certainly look to Obara-Saika or other efficient schemes, but for the time being the goal is to implement BO-MD and not to have an efficient code! ; ) – user23061 Nov 25 '15 at 23:49

My advice is to implement the Obara-Saika recurrence formulae that are outlined in "Molecular Electronic-Structure Theory" by Helgakar, et al. I would stick with Cartesian functions, since a) they are easier and b) spherical harmonics don't matter for molecules anyway.

I did this years ago (in Mathematica) when I was in a similar place -- having completed Szabo and Ostlund and wanting an arbitrary "angular momentum" code.

The book will cost you a small fortune, but if you can borrow it through Interlibrary Loan, it is a phenomenal text.

• I will certainly look at this book, thank you! – user23061 Nov 24 '15 at 23:09
• Unfortunately your suggestions on Boys function does not solve this problem (as I hoped). The error should be directly in the computation of two-electron integrals. I will look to Obara-Saija recurrence. – user23061 Nov 25 '15 at 0:26
• Check normalizations of you basis functions – Eric Brown Nov 25 '15 at 0:29
• Why you suspect about normalization? – user23061 Nov 25 '15 at 1:00
• Did Sij evaluate to 1? – Eric Brown Nov 25 '15 at 1:01

My suggestion would be to use another existing code and run the calculation.

For example, if I do an HF/STO-3G calculation on $\ce{H2O}$, I get:

$$E_\mathrm{H_2O}=-74.9659011\:\mathrm{a.u.}$$

I don't have Cook's book on hand, so I can't look for the error, but I'd suspect some error as you do.

• It will help if I write down explicitly Cook's formulas? I already checked on internet for other HF/STO-3G results and all of them start with -74.96(...) a.u., this is why I am concerned. – user23061 Nov 19 '15 at 9:06
• @R.M. Just because other more modern techniques are efficient does not mean they are inexact. Feel free to post the formulas, but I'd adapt a different method. – Geoff Hutchison Nov 19 '15 at 14:52
• @Goeff I know there are very good (and efficient) techniques, but this will be the next step in my project. At the beginning I just want to code the simplest algorithm possible, even if it is inefficient. Cook's analytical solution only imply a series of loop, which is extremely easy and straightforward to implement (in addition, this is how I implemented the other integrals). However, if I will not find an analytical solution quickly, I will certainly spend some time to implement a more difficult technique. – user23061 Nov 19 '15 at 15:13


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Solve the equation $a^x + b^x = 1$ where $0< a, b < 1$ and $a + b < 1$, in the special cases:
(i) $a = b\quad$ (ii) $a = {1\over 2}, \ b={1\over 4}\quad$
You can find exact solutions to the equation $a^x + b^x = 1$ in special cases like (i) and (ii).
More generally you will need to use a numerical method for finding approximate solutions. See Equation Attack.


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# OutOfBounds Exception when creating a PolygonShape using jbox2d

So here's the deal, i'm parsing a file that contains the vertices for a polygon, that i want to create in box2d. I create a new PolygonShape() and then call .set() giving it a defined array of Vec, and that defined array's .length property. I expected this to work, since the documentation for jbox2d says this method takes a Vec array, and the count of Vec objects in that array. However, it errors out, and it seems to be unrelated to my code. The error i get is

Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 8
at org.jbox2d.collision.shapes.PolygonShape.set(PolygonShape.java:174)
and, upon looking at that line in the jbox2d svn repository, i still cannot figure out the issue.

Any help is appreciated!

• Looking at line 174: int[] hull = (intPool != null) ? intPool.get(Settings.maxPolygonVertices) : new int[Settings.maxPolygonVertices]; It looks like the problem is that intPool is not null and its size is less than maxPolygonVertices. That intPool is null if called from public final void set(final Vec2[] vertices, final int count) - are you calling the public final void set(final Vec2[] verts, final int num, final Vec2Array vecPool, final IntArray intPool) version and if so what value is being sent in for intPool? Dec 9 '12 at 2:51
• i don't believe i'm using that 2nd set method. I appear to be using the first. I'm doing the following PolygonShape pshape = new PolygonShape(); pshape.set(vertices, vertices.length); b.createFixture(pshape, 0); where b is a properly created (using World.createBody(BodyDef)) body. where vertices is a properly filled and sized Vec[]. Dec 9 '12 at 20:16

Your problem is that you are trying to create a PolygonShape with more than 8 vertices. Box2D, and thus JBox2D, default to a maximum of 8 vertices per polygon. This is why you don't get an ArrayIndexOutOfBoundsException until index 8 (0 based indexing means it's vertex #9).
You can change the maximum number of vertices by simply modifying org.jbox2d.common.Settings.maxPolygonVertices.