1. Example 11.2b Multiple Regression

2. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Background Information n In Example 11.2 we created scatterplots for Bendrix and in Example 11.2a we determined that the variable component of overhead must include both MachHrs and ProdRuns. n We found that there was a positive relationship between Overhead and each of the MachHrs and ProdRuns variables. n However, none of the variables appear to have any time series behavior, and the two potential explanatory variables of MachHrs and ProdRuns do not appear to be related to each other.

3. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 BENDRIX1.XLS n The data collected by the manager appear in this file. n The Bendrix manufacturing data set has two explanatory variables, MachHrs and ProdRuns. n We need to estimate and interpret the equation for Overhead when both explanatory variables, MachHrs and ProdRuns, are included in the regression equation.

4. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Solution n To obtain the desired output we use StatPro/Regression Analysis/Multiple menu item. n We select Overhead as the response (dependent) variable and select MachHrs and ProdRuns as the explanatory (independent) variables. n The dialog box shown here then gives us options of which scatterplots to obtain and whether we want columns of fitted values and residuals placed next to the data set. For this example we will fill it in as shown.

5. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Solution -- continued n The main regression output appears in the next table.

6. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Results n The coefficients in the range C16-C18 indicate that the estimated regression equation is Predicted Overhead = 3997 + 43.45MachHrs + 883.62ProdRuns

7. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Interpretation of Equation n The interpretation of the equation is that if the number of production runs is held constant, then the overhead cost is expected to increase by $43.54 for each extra machine hour; and if the number of machine hours is held constant, the overhead is expected to increase by $883.62 for each extra production run. n The Bendrix manager can interpret $3997 as the fixed component of overhead. The slope terms involving MachHrs and ProdRuns are the variable components of overhead.

8. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Equation Comparison n It is interesting to compare this equation with the separate equations found in the previous example: Predicted Overhead = 48,621 + 34.7MacHrs and Predicated Overhead = 75,606 + 655.1ProdRuns n Note that both coefficients have increased. n Also, the intercept is now lower than either intercept in the single variable equation. n It is difficult to guess the changes that more explanatory variables will cause, but it is likely that changes will occur.

9. 11.111.1 | 11.2 | 11.2a | 11.1a | 11.2b | 12.3 |11.211.2a 11.1a11.2b12.3 Equation Comparison -- continued n The reasoning for this is that when MachHrs is the only variable in the equation, we are obviously not holding ProdRuns constant - we are ignoring it - so in effect the coefficient 34.7 of MachHrs indicates the effect of MachHrs and the omitted ProdRuns on Overhead. n But when we include both variables, the coefficient of 43.5 of MachHrs indicates the effect of MachHrs only, holding ProdRuns constant. n Since the coefficients have different meanings, it is not surprising that we obtain different estimates.