Question

Download the dataset returns.xlsx. This dataset records 83 consecutive monthly returns on the stock of Philip Morris (MO) and on Standard & Poor’s 500 stock index, measured in percent. Investors might be interested to know if the return on MO stock is influenced by the movement of the S&P 500 index. Please be aware that return is defined as new price − old price old price × 100%, so it is always reported as a percentage.

6. Fit a linear regression model for this dataset and verify that the least-squares regression line is ˆy = 0.3537 + 1.1695x. Also record the values of the regression standard error, sample correlation, and coefficient of determination. Interpret the coefficient of determination in context.

7. Calculate a 95% confidence interval for the slope of the regression line. What is the margin of error for this interval? Interpret this interval in context.

8. Perform a hypothesis test to see if there is a linear relationship between the two variables. Be sure to write the null and alternative hypotheses, calculate the test statistic, find the p-value and critical value, and state an appropriate conclusion. Round to 4 decimal places.

9. Calculate a 95% confidence interval for the mean monthly returns on the stock of Philip Morris when the S&P stock index is 3.0. Interpret this interval in context.

10. Calculate a 95% prediction interval for the monthly return on the stock of Philip Morris when the S&P stock index is 3.0. Interpret this interval in context.

MO	S&P
-5.7	-9
1.2	-5.5
4.1	-0.4
3.2	6.4
7.3	0.5
7.5	6.5
18.6	7.1
3.7	1.7
-1.8	0.9
2.4	4.3
-6.5	-5
6.7	5.1
9.4	2.3
-2	-2.1
-2.8	1.3
-3.4	-4
19.2	9.5
-4.8	-0.2
0.5	1.2
-0.6	-2.5
2.8	3.5
-0.5	0.5
-4.5	-2.1
8.7	4
2.7	-2.1
4.1	0.6
-10.3	0.3
4.8	3.4
-2.3	0.6
-3.1	1.5
-10.2	1.4
-3.7	1.5
-26.6	-1.8
7.2	2.7
-2.9	-0.3
-2.3	0.1
3.5	3.8
-4.6	-1.3
17.2	2.1
4.2	-1
0.5	0.2
8.3	4.4
-7.1	-2.7
-8.4	-5
7.7	2
-9.6	1.6
6	-2.9
6.8	3.8
10.9	4.1
1.6	-2.9
0.2	2.2
-2.4	-3.7
-2.4	0
3.9	4
1.7	3.9
9	2.5
3.6	3.4
7.6	4
3.2	1.9
-3.7	3.3
4.2	0.3
13.2	3.8
0.9	0
4.2	4.4
4	0.7
2.8	3.4
6.7	0.9
-10.4	0.5
2.7	1.5
10.3	2.5
5.7	0
0.6	-4.4
-14.2	2.1
1.3	5.2
2.9	2.8
11.8	7.6
10.6	-3.1
5.2	6.2
13.8	0.8
-14.7	-4.5
3.5	6
11.7	6.1
1.3	5.8

Answer 1