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Unformatted text preview: 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 2 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 robbers height may be improved by using his shoe size. 55 60 65 70 75 80 4 5 6 7 8 9 101112131415 Shoe Size Inches Statistics 528  Lecture 8 2 Statistics 528  Lecture 8 Prof. Kate Calder 3 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 4 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 3 Statistics 528  Lecture 8 Prof. Kate Calder 5 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
 Statistics, Correlation

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