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# Regression analysis

## Introduction

❶Gauss published a further development of the theory of least squares in , [9] including a version of the Gauss—Markov theorem.

## What is 'Regression'

But before you start that, let us understand the most commonly used regressions:. It is one of the most widely known modeling technique. Linear regression is usually among the first few topics which people pick while learning predictive modeling. This task can be easily accomplished by Least Square Method. To know more details about these metrics, you can read: Model Performance metrics Part 1 , Part 2.

Here the value of Y ranges from 0 to 1 and it can represented by following equation. Above, p is the probability of presence of the characteristic of interest. And, it is logit function. A regression equation is a polynomial regression equation if the power of independent variable is more than 1.

The equation below represents a polynomial equation:. In this regression technique, the best fit line is not a straight line. Some of the most commonly used Stepwise regression methods are listed below:.

The aim of this modeling technique is to maximize the prediction power with minimum number of predictor variables. It is one of the method to handle higher dimensionality of data set. Ridge Regression is a technique used when the data suffers from multicollinearity independent variables are highly correlated.

By adding a degree of bias to the regression estimates, ridge regression reduces the standard errors. It can be represented as:. In a linear equation, prediction errors can be decomposed into two sub components. Look at the equation below. In this equation, we have two components. This is added to least square term in order to shrink the parameter to have a very low variance.

In addition, it is capable of reducing the variability and improving the accuracy of linear regression models. Look at the equation below: ElasticNet is hybrid of Lasso and Ridge Regression techniques. Elastic-net is useful when there are multiple features which are correlated. Lasso is likely to pick one of these at random, while elastic-net is likely to pick both.

Life is usually simple, when you know only one or two techniques. One of the training institutes I know of tells their students — if the outcome is continuous — apply linear regression.

If it is binary — use logistic regression! However, higher the number of options available at our disposal, more difficult it becomes to choose the right one. A similar case happens with regression models.

By now, I hope you would have got an overview of regression. These regression techniques should be applied considering the conditions of data. One of the best trick to find out which technique to use, is by checking the family of variables i. In this article, I discussed about 7 types of regression and some key facts associated with each technique. Hi Sunil, Really a nice article for understanding the regression models. Especially for novice like me who are stepping into Analytic.

Hi Sunil Thanks for posting this. Very nice summary on a technique used so often but underutilised when looking at the different forms available. You wouldnt be interested in doing something similar for classification techniques.. Thanks Tom…you can refer article on most common machine learning algorithms http: Here I have discussed various types of classification algorithms like decision tree, random forest, KNN, Naive Bayes…. The difference given between linear regression and multiple regression needs correction.

It did help me broaden my perspective regarding the regression techniques specially ElasticNet ,but still it would be nice to elucidate upon the differences between l1 and l2 regularization techniques. Though it could be incorporated into a new article I think.

If I print from IE, the only browser allowed on my network, all the ads and hypertext links cover the article text; you cannot read the article. I had suggested having a feature where you use a button to convert the article to a PDF, which can them be printed without the ads and hypertext.

You did in once, then stopped. Read this article to understand the effect of interaction in detail. Hi sunil, The article seems very interesting. Please can you let me know how can we implement Forward stepwise Regression in python as we dont have any inbuilt lib for it.

Thanks fo the guide. And it is performed by making several successive real regression technics linear, polynomial, ridge or lasso…. Are there any specific types of regression techniques which can be used for a time series stationary data? Very nice article, crisp n neat!

The regression analysis creates the single line that best summarizes the distribution of points. Mathematically, the line representing a simple linear regression is expressed through a basic equation: Additionally, a 0 is the y-intercept the value of Y when X is zero and a 1 is the slope of the line, characterizing the relationship between the two variables.

To see why OLS is logical, imagine a regression line running 6 units below one data point and 6 units above another point; it is 6 units away from the two points, on average. Now suppose a second line runs 10 units below one data point and 2 units above another point; it is also 6 units away from the two points, on average.

But if we square the distances involved, we get different results: Additional methods, besides OLS, can find the best line for more complex forms of regression analysis.

The closer a line is to the data points, overall, the stronger the relationship. Regression analysis, again, establishes a correlation between phenomena. But as the saying goes, correlation is not causation. Even a line that fits the data points closely may not say something definitive about causality. Perhaps some students do succeed in French class because they study hard. Or perhaps those students benefit from better natural linguistic abilities, and they merely enjoy studying more, but do not especially benefit from it.

Perhaps there would be a stronger correlation between test scores and the total time students had spent hearing French spoken before they ever entered this particular class. The tale that emerges from good data may not be the whole story. So it still takes critical thinking and careful studies to locate meaningful cause-and-effect relationships in the world. But at a minimum, regression analysis helps establish the existence of connections that call for closer investigation.

Economics , Explained , Mathematics. I hope this kind of thing "Explained" becomes a regular feature. Even if we learned about things like regression in school, it is easy to forget if you don't use it regularly.

Please it is a humble request. Many thanks in advance. Hess Medal Protein analysis uncovers new medulloblastoma subtypes Students invade Killian Court for epic water war.

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## Main Topics

Regression Analysis Regression analysis is a quantitative research method which is used when the study involves modelling and analysing several variables, where the relationship includes a dependent variable and one or more independent variables.

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Regression analysis. It sounds like a part of Freudian psychology. In reality, a regression is a seemingly ubiquitous statistical tool appearing in legions of scientific papers, and regression analysis is a method of measuring the link between two or more phenomena.