Question

A multiple linear regression model based on a sample of 17 weeks is developed to predict standby hours based on the total staff present and remote hours. The SSR is 20,905.02 and the SSE is 25,434.29. (use 0.05 level of significance)

H0​: B1 = B2 = 0

H1​: At least one Bj does not equal 0, j = 1, 2

1. Calculate the test statistic.

Fstat= _____

2. Find the p-value.

p-value= _____

3. Compute the coefficient of multiple​ determination, r2​, and interpret its meaning.

4. Compute the adjusted r2.

Answer 1

we have

ANOVA
	df	SS	MS	F	p value
Regression	2	20905.02	10452.51	5.753459	0.01501
Residual	14	25434.29	1816.735
Total	16	46339.31

H0​: B1 = B2 = 0

H1​: At least one Bj does not equal 0, j = 1, 2

1. Calculate the test statistic.

Fstat= 5.7535

2. Find the p-value.

p-value= 0.01501

3. the coefficient of multiple​ determination, r2​, =SSr/SST =20905.02/46339.31 =0.4511

about 45.11% variation in  standby hours can be explained by the total staff present and remote hours

4. the adjusted r2. = = 0.3727