1Statistics: An IntroductionFifth Edition584Section 16: RegressionA. IntroductionRegression– Use scores from one variable to predict scores on a second variable.Examples:Predict Income from educationPredict college grades from ACT test scoresPredict college grades from high school gradesPredict reading test scores from math test scores585Section 16: RegressionExample Data from Section 14StudentMathReading 150452455036055470605604063035740408505594035104060
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2586Section 16: RegressionShow data as a Scatter DiagramStudents with high math scores tend to have high reading scores. But, relationship not perfect.587Section 16: RegressionRefer to Data - OptionsCould 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=45What is average Math score for people with reading score of 50? (45+55)/2=50Could use these averages as predicted values. Problem: Each prediction based on small number of scores.588Section 16: RegressionCould 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.