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Lecture 19

ADM2304 Lecture 19: 19

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University of Ottawa
Tony Quon

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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