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 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 B0 and B1.

The estimate of B0 is _______

(Round to four decimal places as needed)

The estimate of B1 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 a=0.10 level of significance. Choose the correct answer below.

State the null and alternative hypotheses.

A) H0: B1=0

H1: B1> 0

B) H0: B0=0

H1: B0 =/ (not equal) 0

C) H0: B1=0

H0: B1 =/ (not equal) 0

D) H0: B0=0

H1: B0 > 0  

Determine the P-value for this hypothesis test.

P-value = _____ (Round to three decimal places as needed)

State the approperiate conclusion at the a=0.10 level of significance. Choose the correct answer.

A) 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

B) Reject H0. There is not sufficient evidence to conlcude 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 sufficient evidence to conclude that a linear relation eists between the rate of return of the index and the rate of return of the company stock.

D) 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) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slop 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%?

The mean rate of return for the company stock if the rate of return of the index is 3.25% is ______%

(Round to three decimal places as needed)

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression with Confidence Interval at 90%.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6541
R Square	0.4278
Adjusted R Square	0.3563
Standard Error	3.3871
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	68.6288	68.6288	5.9819	0.0402
Residual	8	91.7822	11.4728
Total	9	160.4110
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	1.4221	1.1260	1.2630	0.2422	-1.1744	4.0185	-0.6717	3.5159
Rates of Return of the index	0.8292	0.3390	2.4458	0.0402	0.0474	1.6109	0.1987	1.4596

a) B0 = 1.4221

B1 = 0.8292

b) H0: B1=0

H0: B1 =/ (not equal) 0

p-value = 0.040

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

c) Lower bound: 0.1987

Upper bound: 1.4596

d) y = 1.422 + 0.829x

rate of return of the index = 3.25%

rate of return for the company stock = 1.422 + 0.829*3.25 = 4.116%