model building overview types of polynomial models second order (quadratic) model example...
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2 nd Order Quadratic Model Example, 15.5 page 579TRANSCRIPT
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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
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Model Building Overview
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2nd Order Quadratic Model Example, 15.5 page 579
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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.
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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:
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Interaction Example, Horsepower, Weight, and Miles Per GallonBasic Assumptions Check
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HPLow, 68 HPHigh, 105
WeightLow, 2194
WeightHigh, 3246
Interaction Example, Horsepower, Weight, and Miles Per GallonInterpreting the interaction
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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
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Example: Estimating the Selling Price of Homes
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NewModel
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Attendance Example
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Attendance Example
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Attendance Example, Analysis and Interpretation
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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.