1. 1 Forecasting/ Causal Model MGS 8150

2. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment Delphi Method Grassroots

3. 3 Causal Models: Causal Model Year 2000 Sales Price Population Advertising …… Time Series Models: Time Series Model Year 2000 Sales Sales 1999 Sales 1998 Sales 1997 …… -- Forecasting based on data and models Quantitative Forecasting

4. 4 Causal versus Correlation There is some confusion between causality and correlation. All causality has some correlation; but all correlations do not indicate causality.

5. 5 Causal forecasting Regression  Find a straight line that fits the data best.  y = Intercept + slope * x  Slope = change in y / change in x Best line! Intercept

6. 6 Causal Forecasting Models Curve Fitting: Simple Linear Regression –One Independent Variable (X) is used to predict one Dependent Variable (Y). –Prediction line is written as: Y = a + b X, where a is the Intercept of the line and b is the Coefficient. –a and b are estimated by software (say, Excel). No need to learn formulas for them. Find the regression line with Excel Use Excel’s Data | Data Analysis | Regression (You may need a plug-in Analysis Tool Pack) Curve Fitting: Multiple Regression –Two or more independent variables are used to predict the dependent variable: Y = b 0 + b 1 X 1 + b 2 X 2 + … + b p X p

7. 7 Using of the Model Make a forecast or prediction Interpretation of the coefficients of X (aka, independent variables) Interpretation of the intercept (optional)

8. 8 Evaluating Goodness of the Model Check the following – –Check R-squared (for the whole model). Indicates how much of the total sum of squared (SS column in the Excel output) is explained away or removed by the Regression model. R-squared = SS Regression/ SS Total. Higher the better … absolute acceptable values depend on the knowledge level of the field –Check F-value and its significance (for the whole model). F-value indicates overall goodness of the model. Higher the better. Check its significance value, simply put, is the probability that the model is not a good fit. Lower the better. –Check p-values (for the individual variables) P-value of a variable, simply put, is the probability that the variable is not a significant player in the model. Lower the better.