# 5.) Hypothesis Testing Flashcards

The F-Test is …if th

a formal hypothesis test that is designed to deal with a null hypothesis that contains multiple hypotheses or a single hypothesis about a group of coefficients

The first step in the F-test is…

translate the particular null hypothesis in question into constraints that will be placed on the equation

A constrained equation can be thought of as…

what the equation would look like if the null hypothesis were correct

For a constrained equation you…

substitute the hypothesized values into the regression equation in order to see what would happen if the equation were constrained to agree with the null hypotest

In the F-test the null hypothesis always leads to a…

constrained equations, even if this violates our standard practice that the alternative hypothesis contains what we expect is true

The second step in an F-test is to…

estimate this constrained equation with OLS and compare the fit of this constrained equation with the fit of the unconstrained equation

If the fits of the constrained equation and the unconstrained equation are not significantly differerent…

the null hypothesis should not be rejected

RSS =

Residual sum of squares from the unconstrained equation

RSS(M) =

residual sum of squares form the constrained equation

M =

number of constraints place don the equation (usually equal to the number of betas eliminated from the unconstrained equation)

(N-K-1) =

degrees of freedom in the unconstrained equation

F =

((RSSm-RSS)/M) / (RSS/(N-K-1))

RSS(M) is always …

greater than or equal to RSS

Imposing constraints on the coefficients instead of allowing OLS to select their values …

can never decrease the summed squared residuals

As the difference between the constrained coefficients and the unconstrained coefficients increases…

the data indicate that the null hypothesis is less likely to be true

The decision rule to use in the F-test is …

to reject null hypothesis if the calculated F-value from Equation 11 is greater than the appropriate critical F-value

The F-statistic has two types of degrees of freedom…

- ) The degrees of freedom for the numerator of Equation 11 (M, the number of constraints implied by the null hypothesis)
- ) The degrees of freedom for the denominator of the F equation (N-K-1 , the degrees of freedom in the regression equation)