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Lecture 19

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ADM2304 Lecture 19: 19
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University of Ottawa

Administration

ADM2304

Tony Quon

Fall

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Regression Towards the Mean
This phenomenon is quite common and has been called “regression towards the mean”
That is the prediction tends to be less removed from the mean than the independent
variable
Examples:
Tall fathers have tall sons but not quite as tall as themselves and short fathers tend to
have short sons but not quite as short as themselves
Students who do well on the midterm tend to do well on the ﬁnal but not quite as well
and students who do poorly on the midterm tend to do poorly on the ﬁnal but not quite
as poorly.
There is an explanation for the ﬁrst example (namely the confounding factor is the
mother’s height) but not for the second…
Pitfalls:
Extrapolation is the use of a regression line for prediction far outside the range of values
of the explanatory variable X used to obtain the line
Such predictions are often inaccurate A lurking variable is a variable that is not among the explanatory or response variables
in a study and yet may inﬂuence the interpretation of relationship among those variables
Two variables are confounded when their effects on a response variable cannot be
distinguished from each other
The confounded variables may either be explanatory variables or lurking variables
Inference for Simple Linear Regression
Recall Least Squares Regression:
Find the the straight line that “best ﬁts” the data
That is, the straight line that minimizes the squared sum of all the deviations from the
actual data points and the line
Population Modei: y0= 1 iβ

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