Question

Case Y X1 X2 X3 X4 X5 X6

1 43 45 92 61 39 30 51

2 63 47 73 63 54 51 64

3 71 48 88 76 69 68 70

4 61 35 86 54 47 45 63

5 81 47 85 71 66 56 78

6 43 34 51 54 44 49 55

7 58 35 70 66 56 42 67

8 71 41 64 70 57 50 75

9 72 31 81 71 69 72 82

10 67 41 78 62 49 45 61

11 64 34 65 58 60 53 53

12 67 41 72 59 41 47 60

13 69 25 61 55 44 57 62

14 68 35 75 59 47 83 83

15 77 46 75 79 74 54 77

16 81 36 52 60 74 50 90

17 74 63 77 79 71 64 85

18 65 60 78 55 77 65 60

19 65 46 83 75 59 46 70

20 50 52 76 64 56 68 58

1. What is the regression equation? (Perform a Multiple Regression Analysis and Paste the table in the first answer box.) 2. State the hypotheses to test for the significance of the independent factors. 3. Which independent factors are significant at alpha= 0.05? Explain. 4. State the hypotheses to test for the significance of the regression equation. Is the regression equation significant at alpha=0.05? Explain. 5. How much of the variability in Y is explained by your model? Explain. 6. What tools would you use to check if the model has multicollinearity problems? 7. Does this model have multicollinearity problems? Explain. 8. If you were to propose a simplified model, eliminating some variables, what would it be? Why? 9. What tools would you use to check if the model assumptions are met? 10. Does this model meet the assumptions? Explain.

Answer 1

Regression Analysis: Y versus X1, X2, X3, X4, X5, X6

Method

Rows unused 20

Analysis of Variance

Source      DF   Adj SS   Adj MS F-Value P-Value
Regression   6 1423.42 237.236     4.25    0.014
X1         1    36.29   36.290     0.65    0.435
X2         1    10.98   10.981     0.20    0.665
X3         1     1.12    1.116     0.02    0.890
X4         1   144.09 144.094     2.58    0.132
X5         1     4.84    4.837     0.09    0.773
X6         1   330.53 330.527     5.92    0.030
Error       13   725.58   55.814
Total       19 2149.00

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
7.47089 66.24%     50.65%      22.97%

Coefficients

Term        Coef SE Coef T-Value P-Value   VIF
Constant    14.6     16.6     0.88    0.396
X1        -0.196    0.243    -0.81    0.435 1.82
X2         0.084    0.189     0.44    0.665 1.51
X3        -0.044    0.314    -0.14    0.890 2.34
X4         0.348    0.217     1.61    0.132 2.30
X5        -0.049    0.165    -0.29    0.773 1.39
X6         0.563    0.231     2.43    0.030 2.37

Regression Equation

Y = 14.6 - 0.196 X1 + 0.084 X2 - 0.044 X3 + 0.348 X4 - 0.049 X5 + 0.563 X6

2)

Ho: b = 0

Ha: b 0

3)

if p-value < 0.05

the variables are significant

here only X6 is significant

4)

Ho: b1 = b2 = ...b6

Ha: not (b1 = b2 = ...b6)

p-value for regression = 0.014 < 0.05

hence the regression equation is significant

5)

this is given by R^2 = 66.24%  

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