文档介绍：Further Inference in the Multiple Regression Model
Joint Hypothesis Testing
The Use of Nonsample Information
Model Specification
Poor Data, Collinearity, and Insignificance
Prediction
Chapter Contents
Economists develop and evaluate theories about economic behavior
Hypothesis testing procedures are used to test these theories
The theories that economists develop sometimes provide nonsample information that can be used along with the information in a sample of data to estimate the parameters of a regression model
A procedure bines these two types of information is called restricted least squares
Joint Hypothesis Testing
A null hypothesis with multiple conjectures, expressed with more than one equal sign, is called a joint hypothesis
Example: Should a group of explanatory variables should be included in a particular model?
Example: Does the quantity demanded of a product depend on the prices of substitute goods, or only on its own price?
Joint Hypothesis Testing
Testing Joint Hypotheses
Both examples are of the form:
The joint null hypothesis in Eq. contains three conjectures (three equal signs): β4 = 0, β5 = 0, and β6 = 0
A test of H0 is a joint test for whether all three conjectures hold simultaneously
Eq.
Joint Hypothesis Testing
Testing Joint Hypotheses
Consider the model:
Test whether or not advertising has an effect on sales – but advertising is in the model as two variables
Testing the Effect of Advertising: The F-Test
Eq.
Joint Hypothesis Testing
Advertising will have no effect on sales if β3 = 0 and β4 = 0
Advertising will have an effect if β3 ≠ 0 or β4 ≠ 0 or if both β3 and β4 are nonzero
The null hypotheses are:
Joint Hypothesis Testing
Testing the Effect of Advertising: The F-Test
Relative to the null hypothesis H0 : β3 = 0, β4 = 0 the model in Eq. is called the unrestricted model
The restrictions in the null hypothesis have not been imposed on the model
It c