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

Model Building Overview

2nd Order Quadratic Model Example, 15.5 page 579

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.

14.47 Interaction Example, Horsepower, Weight, and Miles Per GallonModel to estimate MPG. Is MPG associated with HP, weight, or the interaction of HP and weight?

The Model:

Interaction Example, Horsepower, Weight, and Miles Per GallonBasic Assumptions Check

HPLow, 68 HPHigh, 105

WeightLow, 2194

WeightHigh, 3246

Interaction Example, Horsepower, Weight, and Miles Per GallonInterpreting the interaction

Multicollinearity Assumption

Some of the i.v.’s are highly correlatedIdea; there is redundancy in the i.v.’sResult; 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.’sThrow out redundant i.v.(s)

Example: Estimating the Selling Price of Homes

Example: Estimating the Selling Price of Homes

NewModel

Attendance Example

Attendance Example

Attendance Example, Analysis and Interpretation

Homework (#6)

14.46 Estimating Sales based on Newspaper advertising, Radio advertising, and the interaction1.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$Low, 25

Newspaper$High, 55

Radio$Low, 25

Radio$High, 65

15.7 Estimating county taxes1.Perform a basic assumptions check.2.Use the basic 2nd order model form.3.Do parts a. through i.