For the following partial regression output calculate the fo

For the following partial regression output, calculate the following:

a) R² = R-Square – The Coefficient of Determination.

b) S_YX = Standard Error of the Regression Estimate

c) F_STAT for the overall model, with the degrees of freedom.

d) t_STAT for the population slope, and the critical value of the t-statistic.

e) 95% confidence interval for the population slope and its meaning

SUMMARY OUTPUT

Regression Statistics

Multiple R

R Square

( a )

Adjusted R Square

Standard Error

( b )

Observations

10

ANOVA

df

SS

MS

F

Significance F

Regression

1

359164.6185

( c1 )

Residual

8

39243.70252

Total

9

398408.321

Degrees of Freedom

( c2 )

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-8.30812651

46.68347467

-0.17797

0.863173

-115.9604121

99.34415904

X1

1.57635776

0.184224765

( d1 )

( e )

( e )

Critical t =

( d2)

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square	( a )
Adjusted R Square
Standard Error	( b )
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	359164.6185		( c1 )
Residual	8	39243.70252
Total	9	398408.321
				Degrees of Freedom	( c2 )
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-8.30812651	46.68347467	-0.17797	0.863173	-115.9604121	99.34415904
X1	1.57635776	0.184224765	( d1 )		( e )	( e )
		Critical t =	( d2)

Solution

SUMMARY OUTPUT Regression Statistics Multiple R sqrt(r-sq)=0.9494729 R Square 1-RSS/TSS = 0.90149879 Adjusted R Square 1-MS Res / MS total =0.88918614 Standard Error sqrt(MSE) = 70.0390092 Observations 10 ANOVA df SS MS F Significance F Regression 1 359165 359164.619 73.2172747 2.6822E-05 Residual 8 39243.7 4905.46282 Total 9 398408 44267.5912 Degrees of Freedom 8 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -8.30812651 46.6835 -0.17797 0.863173 -115.960412 99.344159 X1 1.57635776 0.18422 8.5567093 1.2881E-05 1.15153469 2.00118083 Critical t = 2.30600413