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# Dummy Variables Required

Choose Data1 or Data2, and work the following problems:

The number of dummy variables is the number of levels of the categorical variable less one because the one left out is quantified by the intercept. Each coefficient of the dummy variables effects a shift in the intercept to reflect the effect of a different level of the categorical variable. If a categorical variable has 5 levels (A, B, C, D, E), how many dummy variables are required? If the levels are professor, teaching assistant, and student, how many dummy variables are required?

*Layout the selected data for regression by adding a dummy variable for Category and a variable for the interaction of variables Category and X.
*Perform multiple regression analysis of Y on X, the dummy variable, and the interaction variable.
*How significant is the regression model?
*Is the interaction significant?
*If the interaction is significant, can the regression coefficients be interpreted (trick question)?
*Predict Y in the highlighted cells labeled Yhat.
*If the interaction is significant, interpret the regression by examination of a plot of Yhat vs. X with separate series for Categories A and B.
*When interaction is significant, why do we examine group means or a plot of the regression equation instead of interpreting the regression coefficients directly?
*Ignoring the interaction effect, how much does Y change when X changes +1 unit? How much does Y change when Category changes +1 unit?
*Are any of the predictions invalid?

#### Solution Preview

• "b) After running "regression" under "data analysis", if we assume x1 for x, x2 for category and x3 for x*category (interaction variable), then we will have the following equation:
y=11.6303+1.021655x1+0.018965x2-2.0395" - Error
The correct regression equation is: y=11.6303+1.021655x2+0.018965x2-2.03957x3.

1) If a categorical variable has 5 levels (A, B, C, D, E), how many dummy variables are required? If the levels are professor, teaching assistant, and student, how many dummy variables are required?
If a categorical variable has 5 levels, 4 dummy ...

#### Solution Summary

The expert examines the dummy variables required.

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