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. LOADING... 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 0 and beta 1. The estimate of beta 0 is 1.2321. ​(Round to four decimal places as​ needed.) The estimate of beta 1 is 0.7648. ​(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 alphaequals0.10 level of significance. Choose the correct answer below. State the null and alternative hypotheses. A. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 B. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 C. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 Determine the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) State the appropriate conclusion at the alphaequals0.10 level of significance. Choose the correct answer below. A. Reject Upper H 0. 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. Do not reject Upper H 0. 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. Reject Upper H 0. 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 0. 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: 0.2398 ​(Round to four decimal places as​ needed.) Upper​ bound: 1.2898 ​(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​%? The mean rate of return for the company stock if the rate of return of the index is 3.15​% is nothing​%. ​(Round to three decimal places as​ needed.) Click to select your answer(s).

Data Table:

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	3.353.35	5.095.09
​Jun-07	−1.78	0.540.54
​Jul-07	−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	−4.83
​Nov-07	−4.40	−2.38
​Dec-07	−0.86	2.372.37
​Jan-08	−6.12	−4.27
​Feb-08	−3.48	−3.77

PrintDone

Answer 1

Answer: