The data is here. Because this system just accepts the image, I could not upload the data in Excel.

Miles	Age	Price
72.9	12	12.9
7	2	24.8
26.4	1	21
86.4	10	9.7
38.5	5	14.9
51.4	10	13
111	15	10
82.8	9	11.9
33	7	45
23	3	22
115.1	14	4.9
71.2	6	16
78.2	9	9
102	14	8.2
72.7	13	8
8.5	6	32
26.1	1	23
117.4	12	7
61.9	9	7
100.8	8	9

You should answer the following 10 questions:

1. Using appropriate software, produce a scatterplot of Age against Miles in your sample. Compute the sample correlation. What do you think is the reason for the association between the two variables? [2 marks]

2. Set up the null and alternative hypotheses to test whether there is a statistically significant linear association between Age and Miles, taking care to define your notation clearly. [2 marks]

3. Test whether there is a statistically significant linear association between Age and Miles, showing all your steps and clearly stating your conclusion. [2 marks]

The U.S. Department of Transportation's Federal Highway Administration states the average per- son drives around 13,500 miles every year.

4. Use your data to test whether your data support the Department of Transportation's hypothesis. State your assumptions, set up the null and alternative hypotheses, carry out the test, and state your conclusion. [2 marks]

5. Is there any reason to doubt your test result on the average mileage? Explain. [2 marks]

To estimate the relationship between Mustang price and mileage you set up the appropriate regression model.

6. Write down the population regression model taking care to define your notation clearly. Using appropriate software, estimate the regression model and report your results. [2 marks]

7. Interpret the regression slope estimate. [2 marks]

8. Test whether the independent variable is an effective predictor in the estimated regression model. Make sure you report your null and alternative hypotheses, the test statistic, decision rule, and conclusion to the test. [2 marks]

9. Suppose instead of estimating the relationship between price and mileage you estimated the relationship between price and vehicle age. Using appropriate software, estimate the regression model and report your results. [2 marks]

10. In statistics, a proxy variable is a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable. In view of your analysis above, do you think that vehicle age is a suitable proxy for mileage? Explain. [2 marks]

The answering requirements are here below:

1. Produce a clearly labelled plot.

2. State notation and hypotheses.

3. Show your steps and clearly state your conclusion.

4. State notation, hypotheses, test, and conclusion.

5. Keep your answer brief and to-the-point.

6. Show your notation, regression equation, and report regression results using the table, filling in the information in the left-hand (empty) column as appropriate:

	coefficient	std error	t-statistic	p-value

7. Keep your answer to one sentence.

8. State hypotheses, report test results and conclusion.

9. Show your notation, regression equation, and report regression results using the table, filling in the information in the left-hand (empty) column as appropriate:

	coefficient	std error	t-statistic	p-value

10. Keep your answer brief and to-the-point.