Consider the following model that relates the percentage of a household's budget spent on alcohol WALC to total expenditure TOTEXP, age of the household head \(A G E\), and the number of children in the household \(N K\).

Using 1200 observations from a London survey, this equation was estimated with and without the \(A G E\) variables included, giving the following results:

a. Use an \(F\)-test and a \(5 \%\) significance level to test whether \(A G E\) and \(A G E^{2}\) should be included in the equation.

b. Use an \(F\)-test and a \(5 \%\) significance level to test whether \(N K\) should be included in the first equation. [\(F=t^{2}\) ]

c. Use an \(F\)-test, a \(5 \%\) significance level and the first equation to test \(H_{0}: \beta_{2}=3.5\) against the alternative \(H_{1}: \beta_{2} eq 3.5\).

d. After estimating the following equation, we find \(S S E=46086\).

Relative to the original equation with all variables included, for what null hypothesis is this equation the restricted model? Test this null hypothesis at a 5\% significance level.

e. What is the \(\chi^{2}\)-value for the test in part (d)? In this case, is there a reason why a \(\chi^{2}\)-test might be preferred to an \(F\)-test?

Transcribed Image Text:

WALC = + Bln(TOTEXP) + 3NK + B4AGE + BAGE + e