This procedure performs regression with multiple predictors using the least squares method.
1. Choose ProcessMA > Statistics > Regression > Regression (Multiple Predictors)
2. In Response (Y), select the column containing the response data.
3. In Predictors (Xs), select the columns containing the predictors data.
4. Click OK.
Optional
5. Check Fit intercept, to fit a constant term (y-intercept). Otherwise the model will go through the origin.
6. Check Show variance inflation factors. VIF is a measure of multicollinearity (among predictors)
7. Check Show Durbin-Watson statistics. Durbin-Watson statistics detects the autocorrelation in the residuals.
8. Check Show predicted SS and R-Sq, if you want to display the predicted sum of squares and R2.
9. In Predictors for new observations (Xs), select the columns containing new predictors values which you would like to predict the response for.
10. In Confidence level, enter the desired confidence level.
11. Check Plot residuals, if you want to display the residual plots for analysis.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Response (Y): Numeric.
Predictors (Xs): Numeric.
Predictors for new observations (Xs): Numeric.
Confidence level: Numeric; Between 0 to 100.
You know that sales revenue is dependent on the number of sales representative on the field, the amount spend on marketing and the range of products offered. You gathered data from 30 branches and you want to model the relationship and also predict the sales for 2 new branches.
1. Open worksheet ProcessMA > Tools > Data Files > Regression.xls.
2. Choose ProcessMA > Statistics > Regression > Regression (Multiple Predictor).
3. In Response (Y), select C – Sales.
4. In Predictor (X), select D – Reps, E – Marketing, F – Products.
5. Check Fit intercept.
6. Check Show variance inflation factors.
7. Check Show Durbin-Watson statistics.
8. Check Show predicted SS and R-Sq.
9. In Predictors for new observations (Xs), select G – Reps2, H – Marketing2, I – Products2.
10. In Confidence level, enter 95.
11. Click OK.
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Interpretation
The p-values for number of representatives and product range is small, indicating that there is significant evidence that the coefficients of these predictors are not zero. The p-value for amount spent on marketing is 0.874, indicating that there is no significant evidence that its coefficient is not zero. There, the amount spent on marketing will not contribute much to the prediction of sales revenue.
The high VIF values also suggest that the predictors may not be independent. It is possible to simplify the model with lesser number of predictors.
Given the current model, the predicted sale revenue for the two new branches are 1467166 and 1512014 respectively.
You should also analyse and examine the residuals.