How is hypothesis testing used in linear regression?

Hypothesis testing can be carried out in linear regression for the following purposes:

1. To check whether a predictor is significant for the prediction of the target variable. Two common methods for this are as follows:
   1. By the use of p-values:
      If the p-value of a variable is greater than a certain limit (usually 0.05), the variable is insignificant in the prediction of the target variable.
   2. By checking the values of the regression coefficient:
      If the value of the regression coefficient corresponding to a predictor is zero, that variable is insignificant in the prediction of the target variable and has no linear relationship with it.
2. To check whether the calculated regression coefficients are good estimators of the actual coefficients.

The null and alternative hypotheses used in the case of linear regression, respectively, are:

• β1 = 0
• β1 ≠ 0

Thus, if we reject the null hypothesis, we can say that the coefficient β1 is not equal to zero and, hence, is significant for the model. On the other hand, if we fail to reject the null hypothesis, we can conclude that the coefficient is insignificant and should be dropped from the model.