Section 16

# Section 16 - Statistics An Introduction Fifth Edition...

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1 Statistics: An Introduction Fifth Edition 584 Section 16: Regression A. Introduction Regression – Use scores from one variable to predict scores on a second variable. Examples : Predict Income from education Predict college grades from ACT test scores Predict college grades from high school grades Predict reading test scores from math test scores 585 Section 16: Regression Example Data from Section 14 Student Math Reading 1 50 45 2 45 50 3 60 55 4 70 60 5 60 40 6 30 35 7 40 40 8 50 55 9 40 35 10 40 60

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2 586 Section 16: Regression Show data as a Scatter Diagram Students with high math scores tend to have high reading scores. But, relationship not perfect. 587 Section 16: Regression Refer to Data - Options Could predict scores using mean scores on reading for particular scores on math. What is average Reading score for people with Math score of 40? (40+35+60)/3=45 What is average Math score for people with reading score of 50? (45+55)/2=50 Could use these averages as predicted values. Problem: Each prediction based on small number of scores. 588 Section 16: Regression Could draw a line and use the line to make predictions: See Scatterdiagram. Draw a line. What is predicted value for a math score of 40? Of 50? Or 55? How would we have obtained predicted score for a math score of 55 taking averages? Problem: Drawing line by hand subject to error. Depends on person drawing the line.