Question

On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 85%. The standard error of estimate was 12. There were 16 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam.

source	DF	SS	MS
Regression
Error
Total

Answer 1

Given :

The coefficient of determination between the hours studied and the grade earned was 85%.

R^2 = 0.85

The standard error of estimate = 12

ANOVA Table :

source	df	SS	MS	F	P-value
regression	1	355.7647	355.7647	2.471	0.1383
error	14	2016	144
total	15	2371.765

Calculation :

k = 2, N = 16

degrees of freedom for regression :

df1 = k-1 = 2-1 = 1

degrees of freedom for error :

df2 = N-2 = 16-2 = 14

degrees of freedom for total :

dftotal = N-1 = 16-1 = 15

We know that

standard error of estimate = √(SSE / n-2)

12 = √(SSE / 16-2)

12 = √(SSE / 14)

squaring on both sides,

12² = SSE / 14

144 = SSE / 14

144*14 = SSE

SSE = 2016

Also,

R² = SSE / SST

0.85 = 2016 / SST

SST =2016 / 0.85

SST = 2371.765

We have,

SSR + SSE = SST

SSR = SST - SSE

SSR = 2371.765 - 2016

= 355.7647

SSR = 355.7647

MS = SS / df

MSR = SSR / df = 355.7647 / 1 = 355.7647

MSE = SSE / df = 2016 / 14 = 144

F-ratio :

F = MSR / MSE = 355.7647 / 144

= 2.471

F = 2.471

P-value :

P-value corresponding to F = 2.471 with df1 = 1 and df2 = 14 is 0.1383.

P-value = 0.1383 ......(from F table)