Question 1 33 Marks The Data For Question 1 Is Contained In The File A2q1 Csv The File Contains 54 Observations On 1 (85.76 KiB) Viewed 78 times
Question 1 33 Marks The Data For Question 1 Is Contained In The File A2q1 Csv The File Contains 54 Observations On 2 (32.38 KiB) Viewed 78 times
Question 1 (33 marks) The data for Question 1 is contained in the file 'a2q1.csv'. The file contains 54 observations on group averages of households on: total consumption expenditure (total), fraction of expenditure spent on food (fraction), household size (size). Consider the linear regression model fraction = Bo + B total + Basize +u. . 1(a) Do you expect the error term to be homoskedastic? Briefly explain. (3 marks) 1(b) Is there any informal evidence to suggest that the error term may be heteroskedastic? (4 marks) 1(c) Perform the standard White test of the null hypothesis that the conditional variance of the error term in is homoskedastic against the alternative that it is a smooth function of the regressors. Specify any auxiliary regressions that you estimate in answering the question. State the null and alternative hypotheses in terms of restrictions on relevant parameters, specify the form and distri- bution of the test statistic under the null, the sample value and critical value of the test statistic, your decision rule and your conclusion. (8 marks) 1(d) Would it be a good idea to use the White test based on the fitted values in this case? (3 marks) 1(e) Show the line graph of the variable fraction. Is there any informal evidence to suggest that the error term may be serially correlated? (3 marks) 1(f) Perform a Breusch-Godfrey test of the null hypothesis that there is no first-order autocorrelation in the error term in. Specify any auxiliary regressions that you estimate in answering the question. State the null and alternative hypotheses in terms of restrictions on relevant parameters, specify the form and distribution of the test statistic under the null, the sample value and critical value of the test statistic, your decision rule and your conclusion. (8 marks) 1(g) Estimate the linear regression model fraction = Bo + Bitotal + Besize +u by OLS. Correct the standard errors based on the results from the tests in Question 1(c) and 1(f). Compare the results obtained with the usual OLS standard errors to the results with the corrected standard errors. (4 marks)
1 1 1 1 1 1 1 1 1 NNNN 2 2.1 2.1 2.1 2.1 2 3.1 3.1 3.1 3.1 total fraction size 0.0933 0.362272 0.1541 0.347826 0.2248 0.330516 0.2851 0.297089 0.3649 0.323102 0.4213 0.304534 0.4609 0.32046 0.3573 0.368598 0.8973 0.264794 0.1668 0.333333 0.1833 0.358974 0.2689 0.328747 0.3434 0.303727 0.4252 0.284807 0.4914 0.28022 0.5545 0.26817 0.6545 0.262643 1.0499 0.219926 0.2472 0.343851 0.1936 0.383781 0.2952 0.336721 0.3668 0.321701 0.4498 0.298133 0.5333 0.289331 0.5959 0.279913 0.6892 0.279164 1.033 0.237657 0.3102 0.293037 0.2098 0.384652 0.2881 0.381465 0.3726 0.343264 0.4529 0.321925 0.5408 0.306028 0.6243 0.292327 0.7246 0.290229 1.0117 0.254621 0.2251 0.358952 0.203 0.38867 0.2923 0.4013 0.3803 0.363923 0.4658 0.341992 0.5432 0.336156 0.6341 0.307522 0.7528 0.294368 1.2275 0.256212 0.1791 0.502513 mm mmmmmmm 3.1 3.1 3.1 3.1 - 3.1 4.1 4.1 4.1 4.1 4.1 4.1 4 4.1 4 5.2 5.2 5.1 5.1 5.1 5.1 5.1 5.1 5 9 ก เอ o - - -
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