2. Question 2: Using the output from a regression of the log price of car on its

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2. Question 2: Using the output from a regression of the log price of car on its log mileage, say Price log - )(2) Mileage log+error, given in Figure I (a) (10 points) Construct a 95% interval estimate for c(1) and c(2). Please interpret your results b 5 points) Test the hypothesis that (2) is zero against the alternative that it is positive at the 5% significance level. Draw a sketch of the rejection region and the p-value. What is your conclusion? (c) (20 points)Suppose that we now regress the log price of car on its log mileage and an extra dunny variable, say cruise, that is, Price log = c(1)-e(2) * Mileagelog+e(3) * cruise +error. The output of this regression is given in igure 2. Compare this model with the model with the output given in Figure 1. Hint: State clearly the reasons why a model is better than the other one. (5 points)Interpret the resuts of the Durbin-Watson statistics and F-statistics given in Figures 1 and 2. (d)

Explanation / Answer

Here both dependent and independent variables are log transformed.

95% Confidence interval

upper bound

lower bound

upper bound

lower bound

coeffecientC(2)

-0.086769

coeffecientC(1)

10.72537

tinterval

1.646755798

tinterval

1.646755798

SE

0.022172

SE

0.216731

-0.05025713

-0.12328087

11.08227303

10.36847

Calculation of upper bound:

Coefficient +- tint (0.10, n-2) * SE

Interpretation: for $1 increase in mileage, the chance of price to change is between my interval (lower and upper bound)

C(1) = 10.72537

Expected mean value of Y (price) when X =0 (mileage =0)

When mileage was 0, our best guess of car price would be 10.72 percentage points.

Coefficient of C(2) = -0.086769

For this model,. We would conclude that one percentage increase in mileage results in -0.086% change in Price.

b. null hypothesis = 0, alternate hypothesis 0

Our p-value for C(2) = 0.0001

So at 5% level of significance, p value < level of significance (0.05)

We can reject the null hypothesis. It is statistically significant. And therefore mileage is important and to be retained in the regression model. It cannot be eliminated.

upper bound

lower bound

upper bound

lower bound

coeffecientC(2)

-0.086769

coeffecientC(1)

10.72537

tinterval

1.646755798

tinterval

1.646755798

SE

0.022172

SE

0.216731

-0.05025713

-0.12328087

11.08227303

10.36847

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