## Determine the coefficient of determination, Basic Statistics

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A researcher is interested in the relationship between fathers' performance in high school and their children's social skills.  She obtains the high school transcripts of fathers and records their ending GPA. She then measures the social skills of their oldest child.

Use the data shown below to:

A. Calculate the Pearson r correlation coefficient.

B. Test for the significance of the correlation using a two-tailed test at the .05 level.

C. Show the scatterplot for the data.

D. Determine the coefficient of determination and explain what this means.

E. Determine the coefficient of alienation (nondetermination) and explain what this means.

F. Explain to a friend what this correlation coefficient tells you about the relationship between fathers' high school GPA and children's social skills.

G. Explain to your friend what this correlation does not tell you about the relationship between these two variables.  Suggest a third variable that may be a work here.

H. Determine the regression equation.

I. Predict the social skills level of a child whose father had a high school GPA of 2.10.

J. Predict the social skills level of a child whose father had a high school GPA of 3.40.

 Participant Father's GPA Child's Social Skills 1 3.24 65 2 2.68 63 3 2.1 61 4 3.8 67 5 3.26 67 6 3.21 61 7 3.8 70 8 2.5 54 9 2.64 54 10 3.12 58 11 3.08 57 12 3.28 62 13 2.45 59 14 2.83 61

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