Coefficient Estimates and Individual Significance Test
She is analysing the effect of bus fares, income, population and density on demand for urban transportation by bus, so she regresses BUSTRAVL on FARE, INCOME, POP and DENSITY. The EViews output of that estimated model is given in Table 1.
1) Use 5% significance level for all tests.
2) State the null and alternative hypotheses, the test statistic to compute and its distribution, and the criteria for rejecting or failing to reject the null hypothesis for all tests.
a) Interpret the coefficient estimates in Table 1. Perform a (two-tailed) test of individual significance for the parameters of the variables FARE and POP using the critical value of the corresponding distribution and the test p-value. Interpret the test results.
b) Perform an overall significance test for the model in Table 1. What is your conclusion from that test? Provide an interpretation of the value of the coefficient of determination in Table
c) The economist formulates a hypothesis that the effect of the city population density (DENSITY) is five times larger than the effect of the bus fare (FARE), on the variable
BUSTRAVL. Perform a Wald test for the analyst’s hypothesis specifying the null hypothesis and the equation of the restricted model in the knowledge that the sum of the squared residuals (RSS) of the restricted model for that test is 18542143. Interpret the test results.
2 (page 4) plots INCOME (in the X axis) and the estimated residuals (in the Y axis) from the regression in Table 1.
i) Define the classical linear regression model assumption of heteroscedasticity.
ii) Use these plots to graphically test that assumption. Explain your conclusions.
e) The analyst hypothesises that the residuals of the regression present heteroscedasticity. Using the EViews output in Table 2 (on page 5), explain how would the analyst test for heteroscedasticity and what would his conclusion be? Based on your results of that test, what can you say about the properties of the OLS estimator of the model?
f) Is the test performed by the analyst using the information in Table 2 more appropriate for heteroscedasticity than other test available in the literature for that purpose? Justify your answer.
g) Using the estimation results in Table 1: explain how would the analyst test for autocorrelation and what would his conclusion be? Based on your conclusions, comment on the reliability of the OLS estimates and associated statistics in Table 1 and the validity of the test of hypotheses in questions a), b) and c) above.
(a) Clarify the difference between cross-sectional data and time series data. Give examples of each.
(b) State the assumptions of the simple linear regression model and explain why they are necessary.
(c) For the simple linear regression model, when are the estimators of the parameters unbiased, efficient and consistent?
(d) The ‘market model’ of asset returns states that: where and denote the excess return of a stock and the excess return of the market index for the London Stock Exchange. The above model was estimated using time series data for 252 periods (with standard errors in parentheses). = 25 (0.12) (0.13)
(i). Are these coefficients statistically significant and of a reasonable magnitude? Explain the meaning of your findings with regard to the market model.
(ii). Suppose you want to test the null hypothesis that = 0.3 against the two tailed alternative that 0.3. Would you reject the null hypothesis?