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# Coefficeint of Correlation and Coefficient of Determination

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In a study of a 130 female college undergraduates and their parents, each triad of daughter, mother and father completed the UCLA loneliness scale.
a. The correlation between daughter's loneliness score y and mother's loneliness score x was determined to be r = 0.26.
b. The correlation between daughter's loneliness score y and father's loneliness score x was determined to be r = 0.19.
c. The correlation between daughter's loneliness score y and mother's self-esteem score x was determined to be r = 0.14.
d. b. The correlation between daughter's loneliness score y and father's assertiveness score x was determined to be r = 0.01.
e. Calculate the coefficient of determination r2 for parts a-d. Interpret the results.

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https://brainmass.com/statistics/coefficient-of-determination/coefficeint-correlation-coefficient-determination-360021

#### Solution Preview

In a study of a 130 female college undergraduates and their parents, each triad of daughter, mother and father completed the UCLA loneliness scale.
a. The correlation between daughter's loneliness score y and mother's loneliness score x was determined to be r = 0.26.
b. The correlation between daughter's loneliness score y and father's loneliness score x was determined to be r = 0.19.
c. The correlation between daughter's loneliness score y and mother's self-esteem score x was determined to be r = 0.14.
d. b. The correlation between daughter's loneliness score y and father's assertiveness score x was determined to be r = 0.01.
e. Calculate the coefficient of determination r2 for parts a-d. Interpret the results.