For the following partial regression output, calculate the following: a) R 2 = R
ID: 3385885 • Letter: F
Question
For the following partial regression output, calculate the following:
a) R2 = R-Square – The Coefficient of Determination.
b) SYX = Standard Error of the Regression Estimate
c) FSTAT for the overall model, with the degrees of freedom.
d) tSTAT 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)
Explanation / Answer
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
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