Search for question
Question

Q 1 Food expenditure and its determinants have been extensively researched in social

science. We intend to estimate the link between food spending and some of its

factors in this exercise. The data file food.xlsx contains 200 observations for the

following variables from a cross-section of households.

Foodexp: Weekly expenditure on food (excluding restaurants) in dollars.

Income: Weekly household income in dollars.

Children: Number of dependent children living in the household.

Retired: A binary (0/1) indicator of whether head of the household is retired

{ret.-1).

(a) Estimate the following two models and present your summary report for

both models. What do you conclude about the fit of the two models? [4

marks]

(1)

Foodexp = a + a₂ Income + e;

Foodexp = Y₁+ y₂log (Income) + u₂

(b) Now estimate the following regression model and answer all the following

questions.

Foodexp: = Bo + B₁ log(Income;) + B₂ Children; + Retired; + Gi

Estimate the model using Grefl and provide the summary results (Gretl:

Model →Ordinary Least Squares and then select the "Foodexp" as the

dependent variable and "log(Income", "Children" and "Retired" as

Regressors →OK.) (A summary results should include fitted equation with

coefficients, standard error, t-statistic, p-value, sample size, F-statistic and R-

squared). [4 marks]

(c) Does the sign of the slope coefficients agree with your expectations?

Comment. [4 marks]

(d) Comment on the statistical significance of the estimates of the variables,

Income, Children and Retired at 5% significance level. (No need to carry out

hypothesis tests) [4 marks]

(e) Test the overall validity of the regression model at the 5% significance level.

State the hypotheses, restricted and unrestricted model, test statistics and its

distribution when null hypothesis is true, critical value and your conclusion.

[4 marks]

(f) Construct 95% confidence interval for B₁, the slope of the log(Income) variable

and interpret your results. [4 marks]

(g) Based on your answer in part (f), without performing a hypothesis test,

would you reject the hypothesis Ho: B₁ = 90, H₁: ₁90. Clearly states your

conclusion? [4 marks]

(h) Graph the residuals of least squares against log(Income) and describe the

pattern. Do you find any evidence against the violation of any multiple

regression assumptions? Explain. [4 marks]

(i) Test for the existence of heteroscedasticity at the 5% significance level. Use

the White's test (Squares only) and attach your Grefl results. Clearly states all

steps in your test; null and alternative hypotheses, the auxiliary regression

and the test statistic, critical value, your decision and the conclusion. [4

marks]

(i) Based on your findings in part (i), is the model in part (b), valid? How would

you rectify the problem? Attach your Gretl output. Compare your results

with the output in part (b). Comment. [2 marks]

(k) Now run the following regression model:

Foodexp = a₁ + a₂ Income + a₂ Children, + a₂ Retired; + e¡

Compare your model that with part (a). Which model would

And Why? [8 marks]

you

choose?