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 po and beta po1.

The estimate of p0 is ​(Round to four decimal places as​ needed.)

The estimate of p1 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 alphaequals0.10 level of significance.

Choose the correct answer below. State the null and alternative hypotheses.

A. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0

B. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0

C. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0

D. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals

Determine the​ P-value for this hypothesis test. ​P-value ​(Round to three decimal places as​ needed.)

State the appropriate conclusion at the 0.10 level of significance.

Choose the correct answer below.

A. 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.

B. 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. 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. 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)

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 (answer box)

3.25​%? The mean rate of return for the company stock if the rate of return of the index is 3.25​% (​answer box) %. ​(Round to three decimal places as​ needed.)

Month	Rates of return of the​index, x	Rates of return of the company​ stock, y
​Apr-07	4.334.33	3.383.38
​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

Answer 1

data

x	y
4.33	3.38
3.25	5.09
-1.78	0.54
-3.2	2.88
1.29	2.69
3.58	7.41
1.48	-4.83
-4.4	-2.38
-0.86	2.37
-6.12	-4.27
-3.48	-3.77

excel result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.663946888
R Square	0.44082547
Adjusted R Square	0.378694967
Standard Error	3.226678587
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	73.87087131	73.87087131	7.095153696	0.02588949
Residual	9	93.70309232	10.4114547
Total	10	167.5739636
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.239760956	0.985074091	1.258545897	0.239860538	-0.988631456	3.468153368
x	0.766052541	0.287592565	2.663672971	0.02588949	0.115472961	1.416632121

a)
po = intercept = 1.2398
p1 = slope = 0.7661

b)
option D) is correct
Ho : b = 0
Ha: b not equal to 0

p-value = 0.0259

p-value < 0.10(alpha)
hence we reject the null hypothesis

option D) is correct

c)
90% confidence interval for slope =

lower = 0.2389
upper = 1.2932

d)
y^ = 1.2398 + 0.7661*x
when x = 3.25
y^ = 1.2398 + 0.7661*3.25
= 3.7296 %
=3.730 %

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