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Exam 2 Review Regression Prediction Polynomial Regression. Agenda. Prediction. One of the objectives of regression was to be able to predict the behavior of the dependent variable.

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Agenda

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  1. Exam 2 Review • Regression • Prediction • Polynomial Regression Agenda

  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. Prediction (cont.) • 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.

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

  5. Example #2: Y = -.869 + .0611 X1 + .923 X2 where X1 is miles driven, X2 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. Y Y X1 X1 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 + 2X2 + 3X3 +. . . + mXm

  7. Polynomial Regression Example The polynomial regression equation is: SALES = 3.52 + 2.51 ADVERT - 0.0875 ADV2 Predictor Coef Stdev t-ratio p Constant 3.5150 0.7385 4.76 0.000 ADVERT 2.5148 0.2580 9.75 0.000 ADV2 -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 ADV2 • Test whether or not the coefficient for ADV2 is significant. • Predict what sales will be when advertising is 7 (in thousands). • Predict what sales will be when advertising is 15 (in thousands). • Predict what sales will be when advertising is 23 (in thousands).

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