Question 1
Read the given data file cars.xls into EVIEWS, and run a regression of KMLIT against the rest of the variables assuming homoskedastic errors. Copy and paste the EVIEWS output into the space below, and report the estimated equation with the standard errors below the coefficients.
Question 2
Comment on the sign of each estimated coefficient in turn, and state whether this is what you expect. Ignore significance at this stage.
Question 3
Interpret the estimated effect of the engine power (HP) on kilometers travelled.
Question 4
Test whether the data supports the hypothesis that Engine size does affect a car’s mileage (i.e. how far it can travel per litre). Formulate and carry out an appropriate hypothesis test using thet-statistic approach at the 5% significance level.
Question 5
Test whether the number of cylinders affects a car’s mileage. Formulate and carry out an appropriate hypothesis test using the p-values approach, at the 5% level.
Question 6
Test the following hypotheses about the coefficients on CYL (B1) and ENGCM3 (B2). Clearly specify the rejection region if you are using critical values, and clearly state your conclusions. When using p values, calculate and compare your p-values to the test size then state your conclusion.
(Hint, assume the Central Limit Theorem holds)
(a) H0: B1= 0 , H1: B1 > 0, with α=0.05 using the critical-value approach.
(b) H0: B1= 0, H1: B1 < 0, with α=0.05 using the critical-value approach.
(c) H0: B2= 0, H1: B2 > 0, with α=0.05 using the p-value approach.
(d) H0: B2= 0, H1: B2 < 0, with α=0.05 using the p-value approach.
Question 7
Formulate a hypothesis test to test whether a unit increase in a car’s weight (mass) has a greater detrimental effect on fuel efficiency than a unit increase in the power of the car’s engine, rather than the same effect. Use re-parameterization to convert the model to allow you to test this hypothesis using a simple t-test.
Question 8
Verify that the “OLS Wonder Equation” gives a standard error for the CYL coefficient close to 0.145. You will need to run a regression of CYL on all the other independent variables, and you must include this regression output below. (Remember, the OLS Wonder Equation gives an estimate of the homoskedasticity consistent standard error).
Question 9
Test the following joint hypothesis about the coefficients on CYL (B1) and ENGCM3 (B2): H0: and , H1: or , with α=0.05.
Along with the previous results, what do you conclude about B1 and B2? Is this consistent with your intuition?
Question 10
Can you explain any conflict between the implications of the results obtained about and and your expectations? (Hint: Run auxiliary regressions for the explanatory variables in question against the others, and compute the correlations between all the explanatory variables. What do you notice?).