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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Assumptions

Robustness

Model checking

Log transformation (of Y, X, or

both)

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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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PH

4

Create a new variable

ltime=log(time)

Regression analysis

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