Question

In: Statistics and Probability

DATA 2 ID X1 X2 X3 Y A 0 2 4 9 B 1 0 8...

DATA 2

ID X1 X2 X3 Y
A 0 2 4 9
B 1 0 8 10
C 0 1 0 5
D 1 1 0 1
E 0 0 8 10

CORRELATION MATRIX

Y X1 X2 X3
Y 1 ? -0.304 +0.889
X1 ? 1 -0.327 0
X2 -0.304 -0.327 1 -0.598
X3 +0.889 0 -0.598 1

Comparing the zero order model and full model

1. Did the addition of X2 and X3 significantly increase R2? (correct answer is No,p>.01;Type II error is possible, please show me how to get there)

2. What is the adjusted R2 for the full model? (correct answer is 0.742, please show me how to do it)

Solutions

Expert Solution

(1) No,  addition of X2 and X3  increased R2 and it reached to 0.9355 but p-value=0.32 of the regression is greater than 0.01

(2) it is 0.742

Y X1 X2 X3
Y 1.000 -0.348 -0.304 0.889
X1 -0.348 1.000 -0.327 0.000
X2 -0.304 -0.327 1.000 -0.598
X3 0.889 0.000 -0.598 1.000

Regression analysis information has been generated

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.967204
R Square 0.935484
Adjusted R Square 0.741935
Standard Error 2
Observations 5
ANOVA
df SS MS F Significance F
Regression 3 58 19.33333 4.833333 0.319891
Residual 1 4 4
Total 4 62
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 3 2.886751 1.03923 0.487754 -33.6797 39.67965
X1 -2 2 -1 0.5 -27.4124 23.41241
X2 1 1.632993 0.612372 0.650198 -19.7491 21.74915
X3 1 0.322749 3.098387 0.198749 -3.10091 5.10091

orchestra answered 1 year ago
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