Validating the linear regression model

Testing for significance of Regressors

F test

  1. Unrestricted model — In this model, the coefficients of all the explanatory variables are not 0

Testing for linearity in the data set

For checking linearity, we can do the following

  1. Perform Ramsay Reset test to check for linearity of the dataset

Assumptions of Gauss Markov Setup

As we may remember, the assumptions of Gauss Markov setup were that

  1. The residuals belong to a normal distribution
  2. The residuals are homoscedastic

Validating the assumption of normality of residuals

To validate the assumption of normality we have the following tests.

  1. If skewness = 0 and kurtosis = 3 then JB = 0 else JB is not equal to 0

Validating Assumption of Homoscedasticity of residuals

Breusch Pagan test

General inference for the tests

  1. The tests relating to significance of regressors should get rejected as it will signify that the regressors that we have chosen are significant in predicting the target variable
  2. The tests relating to the linearity of dataset should get accepted as it will signify that the data is linear and we can proceed with applying linear regression algorithm to the dataset
  3. The tests relating to normality of residuals should get accepted as it will signify that the residuals are normally distributed which satisfies the assumptions of the Gauss Markov setup under which the linear regression model was built
  4. The tests related to homoscedasticity of residuals should get accepted as it will signify that the residuals are homoscedastic which satisfies the assumptions of the Gauss Markov setup under which the linear regression model was built

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A data science enthusiast currently pursuing a bachelor's degree in data science

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Aayushmaan Jain

A data science enthusiast currently pursuing a bachelor's degree in data science