Q1: An analyst has identified 3 independent variables (X 1 , X 2 , X 3 ) which m
ID: 3309577 • Letter: Q
Question
Q1:
An analyst has identified 3 independent variables (X1, X2, X3) which might be used to predict Y. He has computed the regression equations using all combinations of the variables and the results are summarized in the following table. Why is the R2 value for the X3 model the same as the R2 value for the X1 and X3 model, but the Adjusted R2 values differ?
R2
Adjusted
-R2
Se
0.00089
0.1240
23.5480
0.38700
0.3104
18.4480
0.39100
0.2170
19.6540
0.84130
0.8214
9.3858
0.84130
0.7960
10.0330
0.98630
0.9824
2.9480
0.98710
0.9807
3.0850
X1 does not reduce ESS enough to compensate for its addition to the model.
The standard error for X1 is greater than the standard error for X3.
X1 and X3 represent similar factors so multicollinearity exists.
X1 does not reduce TSS enough to compensate for its addition to the model.
Q2
What goodness-of-fit measure is commonly used to evaluate a multiple regression function?
adjusted R2
R2
total R2
partial R2
IndependentVariable in the
Model
R2
Adjusted
-R2
Se
Parameter Estimates X1
0.00089
0.1240
23.5480
b0 = 93.7174, b1 = 0.922 X20.38700
0.3104
18.4480
b0 = 57.0803, b2 = 1.545 X1 and X20.39100
0.2170
19.6540
b0 = 50.2927, b1 = 1.952, b2 = 1.554 X30.84130
0.8214
9.3858
b0 = 31.6238, b3 = 1.132 X1 and X30.84130
0.7960
10.0330
b0 = 31.133, b1 = 0.148, b3 = 1.132 X2 and X30.98630
0.9824
2.9480
b0 = 14.169, b2 = 0.985, b3 = 0.995 All three0.98710
0.9807
3.0850
b0 = 11.113, b1 = 0.899, b2 = 0.990, b3 = 0.993Explanation / Answer
Q.1 here option (b) and (c) is completely wrong. As addition of factor x1 doesn't affect the model in any way. Coeffiicents are same so no multicollinearlity. So, here Option 1 is correct as X1 does not reduce ESS enough to compensate for its addition to the model.
As TSS = ESS + RSS so TSS will automatically get effected.
So option a is correct.
QUestion 2
Here option B is correct aas Only R2 is used to evaluate a multiple regression function ot test the goodness of fit.
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