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Discussion 11
1 Dummy Variables
Example: Exercise C, Chapter 14, Page 318.
Bars of soap are scored for their appearance in a manufacturing operation. These scores are on a
1-10 scale, and the higher the score the better. The difference between operator performance and
the speed of the manufacturing line is believed to measurably affect the quality of the appearance.
The following data were collected on this problem:
Appearance
Operator Line Speed (Sum for 30 Bars)
1. Using dummy variables, fit a multiple regression model to these data.
2. Using the regression model, demonstrate whether operator differences are important in bar
appearance.
3. Does line speed affect appearance?
4. What model would you use to predict bar appearance?
Scatter plot:
Consider the model
Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 1 X 2 + β 5 X 1 X 3 +
Regression Analysis: Appearance (Y) versus Line Speed (X1), X2, ...
The regression equation is Appearance (Y) = 288 - 0.180 Line Speed (X1) - 16.5 X2 + 52.0 X3 + 0.060 X1*X
Predictor Coef SE Coef T P Constant 287.50 63.23 4.55 0. Line Speed (X1) -0.1800 0.3589 -0.50 0. X2 -16.50 89.42 -0.18 0. X3 52.00 89.42 0.58 0. X1X2 0.0600 0.5075 0.12 0. X1X3 -0.4000 0.5075 -0.79 0.
S = 12.6886 R-Sq = 67.1% R-Sq(adj) = 12.1%
Analysis of Variance
Source DF SS MS F P Regression 5 983.0 196.6 1.22 0. Residual Error 3 483.0 161. Total 8 1466.
Source DF Seq SS Line Speed (X1) 1 322. X2 1 18. X3 1 486. X1X2 1 56. X1X3 1 100.
Consider the model
Y = β 0 + β 1 X 1 + β 4 X 1 X 2 + β 5 X 1 X 3 +
Regression Analysis: Appearance (Y) versus Line Speed (X1), X1X2, X1X
The regression equation is Appearance (Y) = 299 - 0.247 Line Speed (X1) - 0.0330 X1X2 - 0.107 X1X
Predictor Coef SE Coef T P Constant 299.33 31.15 9.61 0. Line Speed (X1) -0.2467 0.1791 -1.38 0. X1X2 -0.03302 0.05017 -0.66 0. X1X3 -0.10685 0.05017 -2.13 0.
S = 10.8253 R-Sq = 60.0% R-Sq(adj) = 36.1%
Analysis of Variance
Source DF SS MS F P Regression 3 880.1 293.4 2.50 0. Residual Error 5 585.9 117. Total 8 1466.
Source DF Seq SS Line Speed (X1) 1 322. X1X2 1 25. X1X3 1 531.
Consider the model
Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 6 X
1 +^
Regression Analysis: Appearance (Y) versus Line Speed (X1), X2, X3, X1^
The regression equation is Appearance (Y) = 984 - 8.13 Line Speed (X1) - 6.00 X2 - 18.0 X3 + 0.0224 X1^
Predictor Coef SE Coef T P Constant 984.0 269.7 3.65 0. Line Speed (X1) -8.133 3.116 -2.61 0. X2 -6.000 6.420 -0.93 0. X3 -18.000 6.420 -2.80 0. X1^2 0.022400 0.008896 2.52 0.
S = 7.86342 R-Sq = 83.1% R-Sq(adj) = 66.3%
Analysis of Variance
Source DF SS MS F P Regression 4 1218.67 304.67 4.93 0. Residual Error 4 247.33 61. Total 8 1466.
Source DF Seq SS Line Speed (X1) 1 322. X2 1 18. X3 1 486. X1^2 1 392.
