Question

The data in the accompanying table represent the rate of return of a certain company stock for 11​ months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts ​(a) through ​(d) below.

Click the icon to view the data table.​(a) Treating the rate of return of the index as the explanatory​ variable, x, use technology to determine the estimates of

beta 0β0

and

beta 1β1.

The estimate of

beta 0β0

is

nothing.

​(Round to four decimal places as​ needed.)

The estimate of

beta 1β1

is

nothing.

​(Round to four decimal places as​ needed.)

​(b) Assuming the residuals are normally​ distributed, test whether a linear relation exists between the rate of return of the​ index, x, and the rate of return for the company​ stock, y, at the

alphaαequals=0.10

level of significance. Choose the correct answer below.

State the null and alternative hypotheses.

A.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1greater than>0

B.

Upper H 0H0​:

beta 1β1equals=0

Upper H 1H1​:

beta 1β1not equals≠0

C.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0not equals≠0

D.

Upper H 0H0​:

beta 0β0equals=0

Upper H 1H1​:

beta 0β0greater than>0

Determine the​ P-value for this hypothesis test.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.) State the appropriate conclusion at the

alphaαequals=0.10

level of significance. Choose the correct answer below.

A.Reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.  

B.Reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

C.Do not reject

Upper H 0H0.

There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.  

D.Do not reject

Upper H 0H0.

There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

​(c) Assuming the residuals are normally​ distributed, construct a​ 90% confidence interval for the slope of the true​ least-squares regression line.

Lower​ bound:

nothing

​(Round to four decimal places as​ needed.) Upper​ bound:

nothing

​(Round to four decimal places as​ needed.) ​(d) What is the mean rate of return for the company stock if the rate of return of the index is

3.153.15​%?

The mean rate of return for the company stock if the rate of return of the index is

3.153.15​%

is

nothing​%.

​(Round to three decimal places as​ needed.)

Click to select your answer(s).

Rate of Return

Month	Rates of return of the​index, x	Rates of return of the company​ stock, y
​Apr-07	4.334.33	3.283.28
​May-07	3.253.25	5.095.09
​Jun-07	negative 1.78−1.78	0.540.54
​Jul-07	negative 3.20−3.20	2.882.88
​Aug-07	1.291.29	2.692.69
​Sept-07	3.583.58	7.417.41
​Oct-07	1.481.48	negative 4.83−4.83
​Nov-07	negative 4.40−4.40	negative 2.38−2.38
​Dec-07	negative 0.86−0.86	2.372.37
​Jan-08	negative 6.12−6.12	negative 4.27−4.27
​Feb-08	negative 3.48−3.48	negative 3.77−3.77

PrintDone

Answer 1

I used R software to solve this problem.

R codes: