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Confidence Interval & Hypothesis Test (L3 - L5) (Prediction (Mean …
Confidence Interval & Hypothesis Test (L3 - L5)
Definition
Confidence Interval
Least-Square Estimator
\beta1
var
expectation
Distribution fo \beta1
CI for \beta1
sigma known
Note: this is a normal distribution
sigma unknown: use MSE to estimate variance
The resulting CI:
Interpretation
Hypothesis Testing
General Form
Test Statistics
Level of Significance
Critical Region Approach
P-value approach
Categories
Two sided
One Sided
Interpretation
Prediction
Purpose
Challenge
Mean Response
Comparison to the estimated regression line
Point estimator
Distributinons
sigma known
sigma unknown
Error in the Prediction of Future Observation
Note: the CI for E(y|x0) only deals with the estimation error of the first part
Prediction Interval
Extrapolation
Def
reasons we should avoid it
F-Test
Usage: F-measure test can be used to test whether the predictor and response variables are associated
Test Statistics: MSR / MSE
Interpretation
Summary
