Scatterplots and Regression
STAT-S 631
Arturo Valdivia
August 31, 2015
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Multicollinearity
STAT-S631
Arturo Valdivia
October 12-14, 2015
Remedial measures
Model (variable) selection (well see this later on)
Principal Component Regression (PCR)
Ridge Regression
Lasso Regression
Center and Scaled Regressors
When using PCR, Ridge
Testing and Analysis of Variance
STAT-S631
Arturo Valdivia
November 6, 2015
Wald Test
Hypothesis testing, where is the estimator of parameter
NH : = 0
AH : = 0
The statistic
t=
0
se()
measures how big the dierence is between the estimator and the parame
Main Eects
STAT-S631
Arturo Valdivia
October 5-7, 2015
Understanding Parameter Estimates
Rate of Change
The rate of change is the usual interpretation of an estimated
coecient
To visualize the eect of a regressor, Xj , x the other
regressors, X(j) , at so
Simple Linear Regression
Arturo Valdivia
September 1, 2015
Simple Linear Regression Model
Two functions dene the model
E (Y |X = x ) = 0 + 1 x
Var (Y |X = x ) = 2
Notation
Uppercase letters, e.g. Y , Yi , Z , denote random variables and
lowercase letters,
Linear Methods for
Regression
Ridge Regression
Least Squares
Subset Selection
Shrinkage Methods
Ridge coefcients minimized a penalized sum of squares
p
p
N
ridge = arg min
(yi 0
xij j )2 +
j2
i=1
j=1
j=1
0 is a complexity parameter controls the amoun