Lecture 2 Linear Regression: A Model for the Mean
Lecture 2
Linear Regression:
A Model for the Mean
Sharyn O¡¯Halloran
Closer Look at:
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Linear Regression Model
Least squares procedure
Inferential tools
Confidence and Prediction Intervals
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U9611
Assumptions
Robustness
Model checking
Log transformation (of Y, X, or
both)
Spring 2005
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Linear Regression: Introduction
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Data: (Yi, Xi) for i = 1,...,n
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Interest is in the probability
distribution of Y as a function of X
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Linear Regression model:
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Mean of Y is a straight line function of X,
plus an error term or residual
Goal is to find the best fit line that
minimizes the sum of the error terms
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Estimated regression line
Steer example (see Display 7.3, p. 177)
Intercept=6.98
7
Equation for estimated regression line:
6.5
.73
Fitted line
^ 6.98-.73X
Y=
6
PH
1
5.5
Error term
0
1
ltime
Fitted v alues
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Spring 2005
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PH
4
Create a new variable
ltime=log(time)
Regression analysis
U9611
Spring 2005
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