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Week 6 - Polynomial regression models, Multicollinearity, Variable Transformation
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Terms in this set (23)
Polynomial regression
A regression model for non-linear relationships; a curvilinear correlation coefficient is computed
R2
The bigger the difference in ____ the better the model's fit over the previous one.
B0 in polynomial
The intercept
B2 in polynomials
The parabola'' concavity. If B2 > 0, the curve opens upwards. Whereas the parabola is convave B2 < 0
Interaction in polynomials
Sinergestic
-Positive sign
Antagonistic
-Negative sign
Second Order Polynomial
Also called cuadratic
Multicollinearity
A situation in which several independent variables are highly correlated with each other. This characteristic can result in difficulty in estimating separate or independent regression coefficients for the correlated variables.
Problems with multicollinearity
Coeffficients cannot be interprated due to unreliable estimates, mainly because of their standard errors.
Signs of the coefficients are not reliable. Usually, are the opposite of that one could expect theorethically.
Statistical tests are biased. t tests and global tests are contradictory.
Variance Inflation Factor (VIF)
a method of detecting the severity of multicollinearity by looking at the extent to which a given explanatory variable can be explained by all the other explanatory variables in the equation
Variable transformation
Different Aims:
- Symetrize distributions
- Stabalize spread
- Linearize relationships between variables
- Normalize distribution
Types of transfromations
Box-Cox
Roots
Powers
others...
QQ-plots
Best tool for verifying departures from normality
Negative skewness (QQ)
Powers (and roots) lower than 1
Positive skewness (QQ)
Powers (and roots) logreaterwer than 1
Low Level of Multicollinearity
1 < VIF < 5
Medium level of multicollinearity
5 < VIF > 10
High level of multicollinearity.
10 < VIF
Tolerance
Alternative to VIF
Center and Standarize
What to do when multicollinearity its found.
partial effect
B1x1
y increases n for every 1 unit increase of x
y ~ income or poly(x,2)1
What would be the prediction based on this formula's output?
y increases n for every 1 unit squared increase of x
y ~ poly(x,2)2
B1
The shift of the parabola. It shifts towards the right when theBcoefficient's value is greater.
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