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 Rates of return of the index-x the company stock-y

Apr-07 4.33 3.38

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.

What is the null and alternative hypotheses?

What is the P-Value for this hypothesis?

(Round to three decimal places as​ needed.)

What is the conclusion from α =0.10 level of significance? Reject or Accept H0? There is or sufficient evidence to conclude linear relation?

​(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 3.15​%?

            (Round to three decimal places as​ needed.)

Answer 1

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