Question

Why does the intercept estimator in simple linear regression follow a normal distribution. Justify this by using the appropriate assumptions of simple linear regression.

Answer 1

In simple Regression equation, we have a dependent variable and a independent variable. Using independent variable, we try to find out the value of depend variable approximately.

It is not possible realistically to estimate in exact form , so there are some errors in the regression model.

The error term can be thought of as the composite of a number of minor influences or errors. As the number of these minor influences gets larger, the distribution of the error term tends to approach the normal distribution. This tendency is called the Central Limit Theorem. The t-test and F- test are not applicable unless the error term is normal distributed.

So , after fitting the model , we apply different test procedures for further studies and to identify the efficiency of the model. It is possible if we assume the intercept terms follows normal distribution.

Assumption related to the distribution of errors are :

1. Errors follows normal distribution with zero mean and equal variance for every observation.

2. Errors are uncorrelated

3. Regression equation must be linear in parameters.