Suppose in the following model
y_i = a_0 + (a_1)(x_1i) + (a_2)(x_2i) + u_1 i = 1,2,....., n
I want to test whether both slope coefficients are zero. In order to derive the restricted residual sum of squares, it is necessary to estimate the following model:
y_1 = a_0 + u_i
Firstly, how can I show that the least squares estimator of a_0 is the sample mean of y_i?
Secondly, how do I derive the relationship between the F test which tests the null given above and R^2?
What are the advantages and disadvantages of R^2? How do I go about explaining if the standard errors of the residuals is better?
This solution provides step by step formula and calculations with explanation, formatted in an attached Word document.