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.

Month   Rates_of_return_of_the_index_-_x   Rates_of_return_of_the_company_stock_-_y
Apr-07   4.33   3.28
May-07   3.25   5.09
Jun-07   -1.78   0.54
Jul-07   -3.20   2.88
Aug-07   1.29   2.69
Sept-07   3.58   7.41
Oct-07   1.48   -4.83
Nov-07   -4.40   -2.38
Dec-07   -0.86   2.37
Jan-08   -6.12   -4.27
Feb-08   -3.48   -3.77

(a) Treating the rate of return of the index as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

The estimate of β0 is

__?__.

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

The estimate of β1 is

__?__.

​(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

α=0.10 level of significance. Choose the correct answer below.

State the null and alternative hypotheses.

A.

H0​: β1=0

H1​: β1≠0

B.

H0​: β0=0

H1​: β0>0

C.

H0​: β0=0

H1​: β0≠0

D.

H0​: β1=0

H1​: β1>0

Determine the​ P-value for this hypothesis test.

​P-value=__?__

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

State the appropriate conclusion at the α=0.10 level of significance. Choose the correct answer below.

A.

Do not reject H0.

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.

B.

Reject H0.

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 H0.

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.

Reject H0.

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.  

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

Lower​ bound:

__?__

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

Upper​ bound:

__?__

​(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 3.45​%?

The mean rate of return for the company stock if the rate of return of the index is 3.45​% is

__?__​%.

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

Answer 1

The statistical software output for this problem is:

Hence,

a) Estimate of Bo = 1.2286

Estimate of B1 = 0.7622

b) Hypotheses: Option A is correct.

P - value = 0.027

c) Lower bound = 0.2343

Upper bound = 1.2901

d) Mean predicted rate = 3.858 %