Statistics 528  Lecture 8
1
Statistics 528  Lecture 8
Prof. Kate Calder
1
Section 2.3: Regression
Idea:
If there is a known linear relationship between two variables x and
y (given by the correlation, r), we want to predict what y might be if
we know x. The stronger the correlation, the more confident we are in
our estimate of y for a given x.
Simple Linear Regression
 fitting a straight line to the data
(mathematical model for the linear relationship b/t two variables)
y = a + bx
Statistics 528  Lecture 8
Prof. Kate Calder
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Example:
The police want to put out a description of a robbery suspect
and they know the shoe size of the suspect from footprints left at the
scene of the crime. Their guess at the robber’s height may be
improved by using his shoe size.
55
60
65
70
75
80
4
5
6
7
8
9 10 1112131415
Shoe Size
Inches
Statistics 528  Lecture 8
Prof. Kate Calder
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Goals of Regression Modeling:
Prediction 
Use the regression line to predict the response y for a
specific value of the explanatory variable x.
Explanation 
Use the regression line to explain the association
between the x and y variables.
Statistics 528  Lecture 8
Prof. Kate Calder
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Extrapolation:
The use of a regression line for prediction far outside the
range of values of the explanatory variable is call extrapolation. Such
predictions are often
inaccurate
.
Statistics 528  Lecture 8
Prof. Kate Calder
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LeastSquares Regression
Which Line?
If points in a scatterplot are widely scattered, how do we know
where to draw the regression line. No line will pass through all the points, but
we want a line that is close as possible to the points.
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 Winter '09
 Calder
 Regression Analysis, Prof. Kate Calder

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