PROBLEM 3-22



Illustration Problem 1

Worksheet

|SUMMARY OUTPUT |

| | | | | |

|Regression Statistics: | | | | |

|Multiple R |0.999105777 | | | |

|R Square |0.998212354 | | | |

|Adjusted R Square |0.997616472 | | | |

|Standard Error |49.83697564 | | | |

|Observations |9 | | | |

|Durbin Watson |1.222 | | | |

| | | | | |

| |Coefficients |Standard Error |t Stat |P-value |

|Intercept |1493.264591 |136.4199931 |10.94608318 |3.45153E-05 |

|Hours |2.605578794 |0.045317358 |57.49626403 |1.85951E-09 |

|Number |13.71420233 |0.916289113 |14.96711261 |5.60187E-06 |

| | | | | |

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|Correlation Matrix: | | | | |

|  |Dollars |Hours |Number | |

|Dollars |1 | | | |

|Hours |0.965126555 |1 | | |

|Number |0.11520857 |-0.145463201 |1 |  |

| | | | | |

Required:

1. Develop the multiple regression equation in general form.

T = 1493.264 + 2.605 X1 + 13.714 X2

2. Can we use the independent variables to predict the dependent variable? Support your answer with the appropriate test.

General Test; t stat > 2 => Yes

Hours: 57.496 > 2 => Yes

Number: 14.967 > 2 => Yes

3. What is the greatest amount of confidence that can be placed in the use of the independent variables to predict the dependent variable? Support your answer with the appropriate test.

Probability Test: 1 – P value = %

Hours: 1 – 0.00000000185 ~ 100%

Number: 1 - 0.00000560 ~ 100%

4. Is multicollinearity and issue with this equation? What decision significance does it have for the regression equation (cite the appropriate statistic)?

Multicollinearity test: r (Xi, Xj ) > 0.8 => Multicollinearity

r (Hours, Number) = [ - 0.145]

r (Hours, Number) < 0.80 => No Multicollinearity

5. What decision significance does the coefficient of determination have for the regression equation (cite the appropriate statistic)?

Adjusted r2 = 0.997

99.7 percent of the variation in the dependent variable is explained by

the variation in the independent variables.

6. What decision significance does the multiple correlation coefficient have for the regression equation (cite the appropriate statistic)?

Multiple R = 0.999

There is an extremely strong direct or positive relationship between

the Independent variables and the dependent variable. Thus, as the

Independent variables increase we strongly expect the dependent

variable to increase also.

7. Perform specification analysis on the regression equation. Are there problems with any of the underlying assumptions of (1) linearity, (2) constant variance of residuals, or (3) independence of residuals? Discuss the results of your analysis.

(1) Linearity - - Examine the line fit plots and offer a conclusion.

(2) Constant variance of residuals - - Examine the residual plots and offer

a conclusion.

(3) Independence of residuals - - Durbin Watson Test

D > du => No Autocorrelation

1.222 < 1.54 => Fails Test

D < dL = Autocorrelation Exists

1.222 < 0.95 => Fails Test

Since dL ≤ D ≤ du => No Conclusion

8. Without regard to the validity of the multiple regression equation developed in requirement 1, develop a 90 percent confidence interval for your estimate of Setup Costs when 2600 setup hours are involved and the plant forecasts 80 setups.

T = 1493.264 + 2.605 (2600) + 13.714 (80)

T = 9,363.384

T ± ( t df = 9 – 2 – 2 = 6 ) ( Se)

a = 0.05

9,363.384 ± (1.943) (49.836)

9,363.384 ± 96.831

Pr (9,266.553 ≤ T ≤ 9,460.215) = 0.90

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