Suppose that in a problem of simple linear regression, a confidence interval with confidence coefficient 1 0 (0 0 1) is constructed for the height of the regression line at a given value of x Show that the length of this confidence interval is shortest when x x ...

Let q be the 1 0 2 quantile of the t distribution n 2 degrees of freedom A confidence in ...

Suppose that in a problem of simple linear regression, a confidence interval with confidence coefficient 1 0

Question:

Suppose that in a problem of simple linear regression, a confidence interval with confidence coefficient 1− α0 (0 < α0 < 1) is constructed for the height of the regression line at a given value of x. Show that the length of this confidence interval is shortest when x = x.