Multivariate Regression . Topics . The form of the equation Assumptions Axis of evil (collinearity, heteroscedasticity and autocorrelation) Model miss-specification Missing a critical variable Including irrelevant variable (s) . The form of the equation. Y t = Dependent variable
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Yt= Dependent variable
a1 = Intercept
b2= Constant (partial regression coefficient)
b3= Constant (partial regression coefficient)
X2 = Explanatory variable
X3 = Explanatory variable
et = Error term
B2 measures the change in the mean value of Y per unit change in X2, while holding the value of X3 constant. (Known in calculus as a partial derivative)
Y = a +bX
dy = b
Correlation exists between
X1 and X2. There is a portion of the
variation of Y that can be attributed to
No correlation exists between
X1 and X2. Each variable explains
a portion of the variation of Y
X2 is a perfect function of X1. Therefore, including X2 would be irrelevant because does not explain any of the variation on Y that is already accounted by X1. The model will not run.
Multicollinearity is related to sample-specific issues
When VIF =1 there is zero multicollinearity, meaning that R2=0
VIF = 1/ (1 – R2 )
Do a regression where the residuals become the dependent
Variable and home value the independent variable.
Let’s regress the predicted value (Y hat) on the log of the residual
(log e2) to see the pattern of heteroscedasticity.
The above pattern shows that our relationships is best described as a
The product of two different error terms Ui and Uj is zero.
Values of the d
d = 4 (perfect negative correlation
d = 2 (no autocorrelation)
d = 0 (perfect positive correlation)
Here we solved the problem of collinearity, heteroscedasticity and
autocorrelation. It cannot get any better than this.
Y (hat) = -7.219+.147(125)+.043(98)
Y (hat) = 15.36