1. regression multiple Dan Fisher Marriott School of Management Brigham Young University November 2005 linear

2. definitions uses of multiple linear regression selection of variables formula application exercise multiple regression analysis summary what will be covered: multiple regression linear

3. multiple regression linear definitions Multiple linear regression is a method of determining the relationship between a continuous process output (Y) and several factors (Xs). Multiple linear regression is a quantitative method of forecasting involving the use of more than one variable to predict some criterion.

4. multiple regression definitions linear Multiple regression differs from simple regression in that it studies the relationship between a single dependent variable and two or more independent variables.

5. uses of multiple linear regression multiple regression linear definitions uses of multiple linear regression selection of variables formula application exercise multiple regression analysis summary

6. multiple regression linear uses of multiple regression There are two major uses for multiple regression: Forecasting Causal analysis

7. multiple regression linear forecasting An estimate of the future level of some variable. We can use forecasting to determine future supply, demand, pricing, sales, or some other variable of interest.

8. multiple regression linear causal analysis Independent variables are regarded as causes of the dependent variable The goal is to determine whether a particular independent variable really affects the dependent variable and how strong that relationship is.

9. multiple regression linear selection of variables definitions uses of multiple linear regression selection of variables formula application exercise multiple regression analysis summary

10. multiple regression linear selection of variables In multiple linear regression we use two primary types of variables: dependent variables and independent variables

11. multiple regression linear selection of variables From the data collected we determine that the main items of interest are as follows: 1.Number of vehicles unloaded 2.Number of different containers (pallets, etc.) handled 3.Total quantity of parts handled Example:Measuring Work in a Warehouse

12. In our warehouse example, the dependent variable is standard hours worked. multiple regression linear dependent variable The dependent variable is the factor that we are trying to measure by using multiple linear regression.

13. multiple regression linear independent variables In multiple regression analysis we will have two or more independent variables. In our warehouse example, the independent variables are: 1.Quantity of vehicles unloaded 2.Quantity of containers handled 3.Quantity of parts handled

14. multiple regression linear formula for multiple regression definitions uses of multiple linear regression selection of variables formula for multiple regression application exercise multiple regression analysis summary

15. multiple regression linear The multiple regression forecast model is defined as follows: where: formula for multiple regression

16. computer software programs are available that can perform complex calculations for us manual calculations are time-consuming and prone to error multiple regression linear computer analysis

17. multiple regression linear application exercise definitions uses of multiple linear regression selection of variables formula for multiple regression application exercise multiple regression analysis summary

18. multiple regression linear application exercise Car Miles Per Gallon Horsepower Engine Displaceme nt 127130112 2288190 33093135 42811397 53190114 6336381 7405561 83010297 9339291 10328190 1129103113 12319097 13337498 143573 152910297 16327889 1728100109 Using a software program capable of regression analysis, such as Microsoft Excel, input the data to the right and analyze the data to determine the relationship between the independent and dependent variables.

19. multiple regression linear definitions uses of multiple linear regression selection of variables formula for multiple regression application exercise multiple regression analysis summary multiple regression analysis

20. multiple regression linear multiple regression analysis dependent variable independent variables dependent variable independent variables

21. multiple regression linear multiple regression analysis R2R2 Coefficients R

22. R 2, the coefficient of multiple determination strength of the relationship between the dependent and independent variables R 2 =.73 multiple regression linear multiple regression analysis Measures of effectiveness

23. R, the correlation coefficient The square root of R 2 R =.86 multiple regression linear multiple regression analysis Measures of effectiveness

24. multiple regression linear multiple regression analysis The equation for the gas mileage example would be in the form below and when plotted would form a plane similar to the one here. where:

25. multiple regression linear the regression coefficients and predicting the dependent variable y Regression coefficients:Regression equation: where: therefore:

26. multiple regression linear definitions uses of multiple linear regression selection of variables formula for multiple regression application exercise multiple regression analysis summary

27. multiple regression linear summary Multiple regression is a statistical tool that management can use in order to create forecasts and perform causal analysis. Multiple regression differs from simple regression in that it studies the relationship between a single dependent variable and two or more independent variables. It is important to select independent variables carefully so that we study the intended relations.

28. multiple regression linear summary Software programs are available that can perform the complex regression calculations for us. The R2 value is an indicator of how well the model fits the data. R tells us how tightly the variables are correlated to one another. By plugging values into the regression equation we end up with a prediction.

29. multiple regression linear readings list: Bowerman, O’Connell, Koehler. Forecasting, Time Series, and Regression 4E. Duxbury, 2005. Golberg, M.A.; Cho, H.A. Introduction to Regression Analysis. WIT Press, 2004. Lewis-Beck, Michael. Applied Regression. Sage Publications, 1980. Allison, Paul D. Multiple Regression: A Primer. Pine Forge Press, 1999. Aguinis, Herman. Regression Analysis for Categorical Moderators. Guilford Press, 2004.