1. Agenda 1.Exam 2 Review 2.Regression a.Prediction b.Polynomial Regression

2. Prediction  One of the objectives of regression was to be able to predict the behavior of the dependent variable.  Prediction: Providing estimates of values of the dependent variable by using the explanatory regression equation: OR:

3.  First need to establish that the model is a good model with strong explanatory power.  We can only use prediction in the region of the data used in the estimation process.  Replace X in the equation with the value for which you want to predict the dependent variable. Prediction (cont.)

4. Example #1: The regression model: Y = 71 + 10 X 1.Is the relationship between X and Y positive or negative? 2.If X is 9, what is y? 3.If X changes one unit, how much does Y change? 4.If X is 0, what is y?

5. Example #2: Y = -.869 +.0611 X 1 +.923 X 2 where X 1 is miles driven, X 2 is no of deliveries and Y is hours of drive time. 1. Predict the total drive time of a driver who needs to make 3 deliveries and travel 70 miles. 2. Predict the total drive time of a drive who still drives 70 miles but now makes 4 deliveries?

6. Polynomial Regression  If the relationship between the dependent and an independent variable is not linear, but curvilinear, then using polynomials may improve the model. Y=  0 +  1 X +  2 X 2 +  3 X 3 +... +  m X m X1X1 Y X1X1 Y

7. Polynomial Regression Example The polynomial regression equation is: SALES = 3.52 + 2.51 ADVERT - 0.0875 ADV 2 Predictor Coef Stdev t-ratio p Constant 3.5150 0.7385 4.76 0.000 ADVERT 2.5148 0.2580 9.75 0.000 ADV 2 -0.08745 0.01658 -5.28 0.000 R-sq = 95.9% R-sq(adj) = 95.4% Analysis of Variance: SOURCE DF SS MS F p Regression 2 630.26 315.13 208.99 0.000 Error 18 27.14 1.51 Total 20 657.40

8. Polynomial Regression (cont.) SALES = 3.52 + 2.51 ADVERT - 0.0875 ADV 2 1.Test whether or not the coefficient for ADV 2 is significant. 2.Predict what sales will be when advertising is 7 (in thousands). 3.Predict what sales will be when advertising is 15 (in thousands). 4.Predict what sales will be when advertising is 23 (in thousands).