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Educational Statistics Copyright © 2014 Robert J. Hall, Ph.D. Simple Linear Regression

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Educational Statistics Anxiety and Performance To measure the relationship between anxiety level and test performance, an educational psychologist obtains a random sample of n = 6 college students from an introductory statistics course. The students are asked to come to the Educational Research and Evaluation Laboratory (EREL) 15 minutes before the final exam. In the lab, the researcher records the physiological measures of anxiety (heart rate, skin resistance, blood pressure, and so on) for each participant. Following the final, the researcher obtained the exam score for each participant. Table 1 summarizes the data.

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Educational Statistics Table 1 StudentAnxiety RatingExam Score A580 B288 C780 D779 E486 F585 Mean583 S.D

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Educational Statistics Scatterplot A B C D E F

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Educational Statistics Slope Calculation

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Educational Statistics Slope Calculation Student Anxiety Rating (X- X)(X- X) 2 Exam Score (Y- Y)(Y- Y) 2 (X- X)(Y- Y) A B C D E F Mean

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Educational Statistics Slope Calculation Student Anxiety RatingX 2 Exam ScoreXY A B C D E F = = 900

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Educational Statistics Slope Calculation Student Anxiety Rating Exam Score A580 B288 C780 D779 E486 F585 Mean583 S.D r xy =-0.89

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Educational Statistics Intercept Calculation StudentAnxiety RatingExam Score A580 B288 C780 D779 E486 F585 Mean583 S.D r xy =-0.89 b yx =-1.78

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Educational Statistics Regression Line for X = 4 for X = 6 Regression Equation

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Educational Statistics Scatterplot (4, 84.78) (6, 81.22)

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Educational Statistics Coefficient of Determination - r 2 xy E A B C D F DATA

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Educational Statistics Coefficient of Determination - r 2 xy Error between Y and Y Error between Y and ^Y Student Anxiety Rating Exam Score^Y (Y- Y)(Y- Y) 2 (Y- ^Y)(Y- ^Y) 2 A B C D E F Mean S.D r xy =-0.89r 2 xy =0.79

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