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.