Question: [16 Marks]

The file "sample_midterm_q3.dat" contains data for 500 households from the 1980-1982 British Family Expenditure Survey. Data have been selected to include only households with two children living in Greater London. The data file contains the following variables:

WFOOD = budget share for food expenditure (defined as expenditure on food / total expenditure)

TOTEXP= total household expenditure (in 10 UK pounds sterling).

A functional form that has been popular for estimating expenditure functions for commodities is

\(WFOOD={{\beta }_{1}}+{{\beta }_{2}}\ln \left( TOTEXP \right)+e\) (1)

1. Estimate the function defined in equation (1) for the households with two children.
2. Interpret the estimated model parameters.
3. Is there an evidence to suggest that increases in total household expenditure increases the budget share of food expenditure? Test at 5% level of significance.
4. Construct a 99% confidence interval for β ₂ and interpret.
5. Find and interpret the measure of goodness of fit.
6. Compute the standard deviation of the residual series?
7. Predict the WFOOD for the household with the total expenditure of 1000 pounds.
8. Compute the slope of the regression that you have estimated in part (a).

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