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:
Response
Regressor or Predictor
Yi = 0 + 1X i + i i = 1,2,!, n
i
( ) i 0, 2
Intercept
Slope 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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