Question

In this chapter, you learn four steps that should be used to evaluate a regression model. What is the first step and why is it important? Explain the other three steps, indicating what you learn from each of those three steps.

Answer 1

The word 'Regression' means 'retrograde motion' or 'going back'.It was first used by the British biometrician Sir Francis Galton(1822-1911) who used this in his study of relation between heights of parents and children. Regression Analysis means  th predition done to check the relationship between two variables , one is the dependent and the other is the independent variable.

There are different kind of regression models;

• Linear Regression
• Logistic regression
• Polynomial regression
• Stepwise Regression
• Ridge Regression
• Lasso Regression

etc...

The type of regression depends on the intensity of the relatiionship between the variable. However the most commonly used regression model is Linear Regression in which the relationship can be easly picturised through a scatter diagram, and the line about which the points in the scatter diagram cluster may be represented by an equation of the form y = a+bx or x = c+dy.

The four main metrices that are used to evaluate regression models are as follows;

• Mean Squared Error(MSE) : It is simply the average of the squared difference between th dependend value and the independent value in the regression model.As it squares the differences, it penalizes even a small error that leads to over estimation of how bad the model is. It is preferred more than other metrices because it is differentiable and hence can be optimized.
• Root Mean squared Error: It is the average square root of the difference between the dependend value and the independent value in a regression model.This is preffered in some cases because the errors are squared before the averaging.
• Mean absolute Error: It is the mean absolute value between the dependend value and independent valu.
• R^2 or coefficient of determination