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

Not what you're looking for?

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?

##### Purchase this Solution

##### Solution Summary

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

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

##### Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

##### Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.