the number of new car sales (nocars) and five assumed related predictor variables pop, Y, price, primert, and unemp over the period from the first quarter of 1976 through the fourth quarter of 1990. Also attached is a set of definitions for the relevant variables. Answer the following questions using the included data set. The data is available in a SHAZAM file on the course Blackboard site, as is the variable definitions.
1. Estimate the regression equation.
2. Provide an interpretation of the coefficients on each independent variable in the estimated regression equation.
3. Perform relevant one-tailed hypothesis tests for the significance of the coefficients on each independent variable. (Your expected sign should be in your alternative hypothesis.) Include the null and alternative hypothesis for each test, the decision rule, the value of the test statistic, the relevant one-tailed p-value (or a note that you got the wrong sign, so the relevant one-tailed p-value is large), and your decision in each case.
4. Report and interpret the values of both R2 and adjusted R2 for the estimated regression.
5. Do a goodness of fit test for this model to see whether it is useful in explaining the observed sample variability in the dependent variable.
6. Analyze the data in this regression model for multicollinearity. State the null and alternative hypothesis that you are testing for in each case, what decision criteria you use, and the decisions you reach about the presence of multicollinearity. Test for both simple multicollinearity between pairs of explanatory variables and higher-order multicollinearity using Klein's Rule of Thumb.
7. Analyze the model for first-order autocorrelation.
A. First do a runs test. Carefully explain what you are testing for. Include your null and alternative hypothesis, any relevant information from the SHAZAM output (which will depend on whether you can do a small sample or a large sample test), the decision rule you use to do the test, including any relevant critical values from the statistical tables, and your decision.
B. Do a one-tailed Durbin-Watson test for the presence of positive autocorrelation (Use the DWPVALUE option in the OLS command). Specify your null and alternative hypothesis, the value of the Durbin-Watson statistic, the p-value for the one-tailed test for positive autocorrelation, and the decision you reach.
8. Test for the presence of heteroscedasticity of the form that the variance of the error term is a linear function of the predicted value of the dependent variable. Specify your null and alternative hypothesis, write out the appropriate decision rule, report the value of the test statistic and the appropriate critical value, and report your conclusion.
Attachment:- carsales.rar