Explore BrainMass

# The F Test and Multiple Regression Model for Two Independent Variable

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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?

© BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
https://brainmass.com/statistics/f-test/the-f-test-and-multiple-regression-model-for-two-independent-variable-12374

#### Solution Summary

This solution provides step by step formula and calculations with explanation, formatted in an attached Word document.

\$2.49