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Crash Testing Data (Crash Testing Data (2nd Issue: Heteroskedasticity…
Crash Testing Data
Crash Testing Data
1st Issue: Multicollinearity
High Correlation between Explanatory Variables
NFL Quarterback Salary Example
Do the coefficient signs meet intuition?
Are variables significant? (2-t Rule of Thumb)
Explore Potential Multicollinearity
Correlation Matrix (High if greater than 0.7)
High Collinearity Leads to High Variance
Test for High Variance with VIF
Consequences of High Variance in an Explanatory Variable
Scatterplot
Brief Regression Review of the b's
Decision Tree for Checking
2nd Issue: Heteroskedasticity
What is a Residual?
Homoskedasticity (Constant Variance of the Residuals)
vs.
Heteroskedasticity (Non-Constant Variance of the Residuals)
Common Example: Spending & Income
Hypothesis Test for Heteroskedasticity: Breusch-Pagan
Remedy for Heteroskedasticity:
Transform Response Variable OR
Weight the Residuals
Check if Residuals are Normal
Data can crash if assumptions are violated
Remedy for Multicollinearity:
Ridge Regression
Avoid Dropping Variable
Ridge does not Use OLS (OLS uses B.L.U.E.)
Ridge cares more about reducing Variance
What High Variance of Coefficients looks like
(unbiased but not-precise/"wild")
Low Variance of Coefficients with Ridge (more precise, but some bias)
Quarterback Data Example (Better Coefficients, Lower Variance)
Example & Remedy of Heteroskedasticity
(Spending & Income)
Visual of Residuals on Income
Regress Spending on Income (is Variance of observations increasing?)
Breusch-Pagan Test for Heterskedasticity
Attempted Remedies:
Transform Spending to Log Form
Weighted Least Squares
All Rights Reserved by Brent Marinan & University of Arizona
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