Question

1. For the following data sample, calculate the sum of squared residuals and standard error of the slope coefficient from a regression of AAPL on SPY.

date	SPY	AAPL
1/1/18	2.46%	3.41%
1/8/18	1.65%	1.19%
1/15/18	0.90%	0.77%
1/22/18	2.20%	-3.89%
1/29/18	-3.88%	-6.42%

1. SSR ___
2. se(slope) ___
3. Calculate the R²
4. Test the null hypothesis that the beta is equal to 1 with a 5% significance level.
5. What is the approximate p-value for the test in d)?

Answer 1

1. For the following data sample, calculate the sum of squared residuals and standard error of the slope coefficient from a regression of AAPL on SPY.

date	SPY	AAPL
1/1/18	2.46%	3.41%
1/8/18	1.65%	1.19%
1/15/18	0.90%	0.77%
1/22/18	2.20%	-3.89%
1/29/18	-3.88%	-6.42%

a.) SSR = 0.0031

b). se(slope) = 0.6113

c). Calculate the R²

         = 0.5306

d). Test the null hypothesis that the beta is equal to 1 with a 5% significance level.

t = (1.1257-1)/0.6113

 = 0.2056

DF = n-2 =3

Table value of t with 3 DF at 0.05 level =3.182

Calculated t = 0.2056 < the table value 3.182

The null hypothesis is not rejected.

There is not enough evidence to conclude that the beta is different from 1.

e). What is the approximate p-value for the test in d)?

P=0.8502

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis
	r²	0.5306	n	5
	r	0.7284	k	1
	Std. Error of Estimate	0.0319	Dep. Var.	AAPL
Regression output						confidence interval
variables		coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	a =	-0.0174	0.0148	-1.171	.3262	-0.065	0.030
SPY	b =	1.1257	0.6113	1.841	.1628	-0.820	3.071
ANOVA table
Source	SS	df	MS	F	p-value
Regression	0.0035	1	0.0035	3.39	.1628
Residual	0.0031	3	0.0010
Total	0.0065	4