Question

i Rate of Return Month Rates of return of the Rates of return of the index, x company stock, y Apr-07 4.23 3.38 May-07 3.25 5.09 Jun-07 - 1.78 0.54 -3.20 2.88 Jul-07 Aug-07 1.29 2.69 Sept-07 3.58 7.41 1.48 -4.83 Oct-07 -4.40 -2.38 Nov-07 2.37 Dec-07 -0.86 -6.12 -4.27 Jan-08 -3.48 Feb-08 -3.77 X

Answer 1

Let's carry out regression between rates of return of index x and that of stock y. In Excel, go to Data tab->Data Analysis->Regression, and choose returns on index x as X-column and returns of stock y as Y-column. We select 90% as the confidence level for the regression. We get the following regression output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.664741084
R Square	0.441880708
Adjusted R Square	0.379867454
Standard Error	3.22363256
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	74.04770173	74.04770173	7.125584856	0.025648537
Residual	9	93.52626191	10.39180688
Total	10	167.5739636
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	1.248840147	0.984653872	1.268303699	0.236513141	-0.978601661	3.476281956	-0.556141599	3.053821893
x	0.76992373	0.288428019	2.669379114	0.025648537	0.117454221	1.42239324	0.241202598	1.298644862

a) Looking at the coefficients in the output, we get:

$\beta_0$ = 1.2488

= 0.7699

31

b) The p-value of the coefficient of stock return x is 0.0256 < 0.1

=> x is a significant predictor of y. Hence, there is a significant linear relationship between x and y at the 0.1 level of significance.

Null and alternative hypotheses are:

H₀: = 0

31

H_a:
31
$\ne$ 0

Hence, C is the correct option.

As seen above from the table, p-value = 0.026