Lecture 12 Linear Regression: Test and Confidence Intervals
Lecture 12
Linear Regression:
Test and Confidence Intervals
Fall
?2013
?
Prof.
?Yao
?Xie,
?yao.xie@isye.gatech.edu
?
H.
?Milton
?Stewart
?School
?of
?Industrial
?Systems
?&
?Engineering
?
Georgia
?Tech
1
Outline
?
?
?
?
Properties
?of
??
?
?
?1
?
?and
??
?
?
?0
?
?as
?point
?estimators
?
Hypothesis
?test
?on
?slope
?and
?intercept
?
Confidence
?intervals
?of
?slope
?and
?intercept
?
Real
?example:
?house
?prices
?and
?taxes
?
2
Regression analysis
? Step
?1:
?graphical
?display
?of
?data
?
?scatter
?plot:
?sales
?
vs.
?advertisement
?cost
?
!
!
!
!
!
!
!
? calculate
?correlation
3
? Step
?2:
?find
?the
?relationship
?or
?association
?between
?
Sales
?and
?Advertisement
?Cost
?
?Regression
4
Simple linear regression
Based on the scatter diagram, it is probably reasonable to assume that the mean of the
random variable Y is related to X by the following simple linear regression model:
Regressor or Predictor
Response
i
(
Yi = 0 + 1 X i + i
i 0, 2
Intercept
)
Slope
i = 1,2,!, n
Random error
where the slope and intercept of the line are called regression coefficients.
?The case of simple linear regression considers a single regressor or predictor x and a
dependent or response variable Y.
5
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