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General Linear Model (GLM)Regression Equations |
The regression equation is an algebraic representation of the regression line and describes the relationship between the response and predictor variables. The regression equation takes the form of:
Response = constant + coefficient * predictor + ... + coefficient * predictor
or y = bo + b1X1 + b2X2 + ... + bkXk
Where:
Minitab provides a single regression equation when the model contains only categorical factors or when there are more than 50 combinations of factor levels.
Example Output |
Regression Equation
Salary = 2.7275 - 0.5775 Subject_1 + 0.0792 Subject_2 + 0.3858 Subject_3 + 0.1125 Subject_4 - 0.3400 Degree_1 - 0.2600 Degree_2 + 0.6000 Degree_3 - 0.0100 Subject*Degree_1 1 + 0.0600 Subject*Degree_1 2 - 0.0500 Subject*Degree_1 3 - 0.0167 Subject*Degree_2 1 - 0.0267 Subject*Degree_2 2 + 0.0433 Subject*Degree_2 3 - 0.0233 Subject*Degree_3 1 - 0.0033 Subject*Degree_3 2 + 0.0267 Subject*Degree_3 3 + 0.0500 Subject*Degree_4 1 - 0.0300 Subject*Degree_4 2 - 0.0200 Subject*Degree_4 3 |
Interpretation |
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For the salary data, Minitab displays a single equation where the response variable is Salary and the predictors are the:
You can interpret the slope value for each categorical factor as the change in salary based on group membership. For a professor with a Master's degree (degree = 2) in the Humanities (subject = 1 ), the variables Subject_1, Degree_2, and Subject*Degree_1 2 take on the value of 1, while the others are 0. Add the constant and the applicable terms to calculate the predicted value:
2.7275 - 0.5775 - 0.2600 + 0.0600 = 1.9500 or $1,950.00
Use Stat > ANOVA > General Linear Model > Predict to calculate the predictions and confidence intervals for predictor values that you specify.