Question: 3. Shown is a partial computer output from a regression analysis: Y X1 X2 X3 100 10 3 10 80 6 6 15 87 7
3. Shown is a partial computer output from a regression analysis:
Y
X1
X2
X3
100
10
3
10
80
6
6
15
87
7
7
8
70
5
10
6
65
4
12
4
77
5
8
6
65
2
14
3
78
6
9
5
90
8
4
12
82
7
5
8
Regression Analysis: y versus x1, x2, x3 . The regression equation is
Y = 61.53 + 3.837X1 - 0.66 X2 - 0.004 X3
Predictor Coef SE Coef T P
Constant 61.53 26.10 2.36 0.057
X1 3.837 1.930 1.99 0.094
X2 -0.660 1.508 -0.44 0.678
X3 -0.004 0.6235 -0.01 0.996
R-Sq = 92.31%
Analysis of Variance (
ANOVA Table
)
Source DF SS MS F P
-----------------------------------------------------------------
Regression ---- ---- 342.79 23.99 0.001
Residual Error ---- ---- ----
----------------------------------------------------------------
Total ---- ----
Stepwise Regression: Y versus X1, X2, X3
Backward elimination.
Response is Y on 3 predictors,
Step 1 2 3
Constant 61.53 61.42 50.49
X1 3.84 3.84 4.82
T-Value 1.99 2.45 9.48
P-Value 0.094 0.044 0.000
X2 -0.66 -0.65
T-Value -0.44 -0.66
P-Value 0.678 0.530
X3 -0.00
T-Value -0.01
P-Value 0.996
S 3.78 3.50 3.37
R-Sq 92.30 92.30 91.82
d) Calculate all of the missing entries.
e) Use the ANOVA table and determine whether there is a significant linear relationship
between Y and at least one of the three explanatory variables at 0.05 level of significance.
c) At the 0.05 level of significance, and stepwise regression determine whether each
explanatory variable makes a significant contribution to the regression model. Based upon these
results, indicate the regression model that should be utilized in this problem.
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