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-18   4.23   3.38
May-18   3.25   5.09
Jun-18   -1.78   0.54
Jul-18   -3.20   2.88
Aug-18   1.29   2.69
Sept-18   3.58   7.41
Oct-18   1.48   -4.83
Nov-18   -4.40   -2.38
Dec-18   -0.86   2.37
Jan-19   -6.12   -4.27
Feb-19   -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 beta 0β0 and beta 1β1.

The estimate of beta 0β0 is? ​(Round to four decimal places as​ needed.)

The estimate of beta 1β1 is? ​(Round to four decimal places as​ needed.)

Determine the​ P-value for this hypothesis test.

​P-value equals=? ​(Round to three decimal places as​ needed.)

​(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 3.25​%?  ​

(Round to three decimal places as​ needed.)

Answer 1

The statistical software output for this problem is:

From above output:

a) β0 = 1.2488

β1 = 0.7699

P - value =  0.026

b) Lower bound = 0.2412

Upper bound = 1.2986

c) Mean rate = 3.751