Question

Derive the formula for a (1-α) level confidence interval for the Mean response E(Y|X=x*) using the simple linear regression model, where x* is a specified value for X.   

Answer 1

Let the simple linear regression model be:

Let be the value of regressor variable for which we wish to estimate the mean response, E(Y|X=). An unbiased point estimator of E(Y|) is given as:

Thus,

We use here,

Thus, the 100(1-) percent confidence interval at X= is obtained as: