A well-known model in finance, called the market model, assumes that the monthly rate of return on a stock (R) is linearly related to the monthly rate of return on the overall stock market (R_m). The mathematical description of the model is

R = ₀ + ₁ R_m +

where the error term is assumed to satisfy the requirements of the linear regression model. For practical purposes, R_m is taken to be the monthly rate of return on some major stock market index, such as the New York Stock Exchange Composite Index.

The coefficient ₁, called the stock's beta coefficient, measures how sensitive the stock's rate of return is to changes in the level of the overall market. For example, if ₁ > 1 (₁ < 1), the stock's rate of return is more (less) sensitive to changes in the level of the overall market than is the average stock. The monthly rate of return for Host International Inc. stock and for the overall market (as approximated by the NYSE Composite Index) over a 5-year period are given below. (The data are stored on Canvas. Column 1 stores the monthly percentage return for Host International, and column 2 stores the monthly percentage return for the NYSE Composite Index. So, for example, a value of R=1 means a 1% return.)

Questions:

a. Is Host International more sensitive than average to overall stock market movements? Perform a formal test.

b. Find a 95% prediction interval for next month's rate of return for Host International stock, given that the corresponding rate of return for the overall market is 0.5%.

c. What proportion of the variability of the return for Host International is explained by overall stock market movements?

host	nyse index
26.7	13.5
7	6.1
15.9	2.9
18.6	4.7
-6	5.5
-4.2	5.2
4	-6.4
-5.2	-2
-1.7	-3.6
28.2	6.1
17.6	3.1
1.6	-1
17.6	12.5
-13.4	0.1
-12.1	3
-6.2	-1.1
-12.1	3
-2.5	4.7
-9.3	-0.7
0	0
-1.5	2.6
-5.3	-2.1
9.7	0.5
18.7	5.8
-10.7	-4
-8.4	-1.6
6.3	-1.1
1.2	0.4
2.5	-1.2
14.3	5.3
-4.2	-1.5
2.2	-1.4
3.1	0.1
6.4	-3.9
11	4.2
-1	0.5
-2.7	-5.7
10.4	-1.2
10.2	3.2
15.6	8.3
5.4	1.9
1.2	-1.3
22.3	5.7
3.1	3.8
-13.6	-0.6
-28.8	-10.2
19	3.1
-2.1	1.6
-7.8	4.7
-10.1	-2.9
11.4	6.2
-5.5	0.7
-6.6	-1.5
19.6	4.5
3.7	1.5
7.9	6.3
-3.2	0
-10.4	-6.9
-12.4	6
-4.2	2.3