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SIMPLE LINEAR REGRESSION
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SIMPLE LINEAR REGRESSION
Documents prepared for use in course
C22.0103.001
,
New York University, Stern School of Business
Fictitious example,
n
= 10.
Page 3
This shows the arithmetic for fitting a simple linear regression.
Summary of simple regression arithmetic
page 4
This document shows the formulas for simple linear regression, including
the calculations for the analysis of variance table.
Another example of regression arithmetic
page
8
This example illustrates the use of wolf tail lengths to assess weights.
Yes, these data are fictitious.
An illustration of residuals
page 10
This example shows an experiment relating the height of suds in a dishpan
to the quantity of soap placed into the water.
This also shows how you
can get Minitab to list the residuals.
The simple linear regression model
page 12
This section shows the very important linear regression
model
.
It’s very
helpful to understand the distinction between parameters and estimates.
Regression noise terms
page 14
What are those epsilons all about?
What do they mean?
Why do we need
to use them?
More about noise in a regression
page 18
Random noise obscures the exact relationship between the dependent and
independent variables.
Here are pictures showing the consequences of
increasing noise standard deviation.
There is a technical discussion of the
consequences of measurement noise in an independent variable.
This
entire discussion is done for simple regression, but the ideas carry over in
a complicated way to multiple regression.
Does regression indicate causality?
page 26
This shows a convincing relationship between
X
and
Y
.
Do you think that
this should be interpreted as cause and effect?
An interpretation for residuals
page 28
The residuals in this example have a very concrete interpretation.
x
1
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SIMPLE LINEAR REGRESSION
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Summary of regression notions for one predictor
page 3
1
This is a quick onepage summary as to what we are trying to do with a
simple regression.
The residual versus fitted plot
page 3
2
Checking the residual versus fitted plot is now standard practice in doing
linear regressions.
An example of the residual versus fitted plot
page 3
6
This shows that the methods explored on pages 3
2
3
5
can be useful for
real data problems.
Indeed, the expanding residuals situation is very
common.
Transforming the dependent variable
page 4
1
Why does taking the log of the dependent variable cure the problem of
expanding residuals?
The math is esoteric, but these pages lay out the
details for you.
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 Spring '08
 CHoi
 Regression Analysis, Standard Deviation, Yi, Errors and residuals in statistics

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