1. Model Building Overview Types of Polynomial Models Second Order (Quadratic) Model Example Interaction Example (cars and speed estimating number of accidents) -Interpretation of interaction with Excel Attendance Example (nominal & continuous i.v.’s) Multicollinearity Assumption Analysis Homework Next up -Introduction to Time Series Analysis

2. Model Building Overview

3. 2 nd Order Quadratic Model Example, 15.5 page 579

4. R-Squared for the quadratic model (0.8623) is greater than R-Squared for the SLR Model (0.7823) and the quadratic term contributes (i.e. there is a significant quadratic association between price and sales). Thus, the quadratic model is a better fit. 86.23% of the variation in price can be explained by the quadratic relationship between sales and price.

5. 14.47 Interaction Example, Horsepower, Weight, and Miles Per Gallon Model to estimate MPG. Is MPG associated with HP, weight, or the interaction of HP and weight? The Model:

6. Interaction Example, Horsepower, Weight, and Miles Per Gallon Basic Assumptions Check

7. HPLow, 68HPHigh, 105 WeightLow, 2194 WeightHigh, 3246 Interaction Example, Horsepower, Weight, and Miles Per Gallon Interpreting the interaction

8. Multicollinearity Assumption Some of the i.v.’s are highly correlated Idea; there is redundancy in the i.v.’s Result; distortions in the model (beta coefficients far away from true values, high standard errors, and more) Test; Generate a correlation matrix among the i.v.’s Throw out redundant i.v.(s) Example: Estimating the Selling Price of Homes

11. New Model

12. Attendance Example

14. Attendance Example, Analysis and Interpretation

15. Homework (#6) 14.46 Estimating Sales based on Newspaper advertising, Radio advertising, and the interaction 1.Perform a basic assumptions check. 2.Perform a basic mulitcollinearity assumption check. 3.Is the overall model useful? (overall F-Test) 4.Perform a test to determine if the interaction is significant. 5.Interpret the interaction, if significant, using a simple graph. -What is the estimation model when amount of Radio advertising spend is low (25)? -What is the estimation model when amount of Radio advertising spend is high (65)? -To develop your graph use the following 2 by 2 table will help, where the interior of the table is estimated sales! Newspaper$L ow, 25 Newspaper$Hi gh, 55 Radio$Low, 25 Radio$High, 65 15.7 Estimating county taxes 1.Perform a basic assumptions check. 2.Use the basic 2 nd order model form. 3.Do parts a. through i.