# Sample Correlation, Intercepts, and the Coefficient of Determination

An analyst believe that the only important determinant of banks' return on assets (Y) is the ratio of loans to deposits (X). For a random sample of banks the sample regression line:

Yhat = 0.97 + 0.57X

1.72 2.04 T statistics

was obtained with the coefficient of determination 0.720.

a. Find the sample correlation between returns on assets and the ratio of loans to deposits.

b. Interpret the intercept and slope of the estimated regression line.

c. Interpret the coefficient of determination.

d. Test the null hypothesis that the slope of the population regression line is 0 against the alternative that the true slope is not equal to zero, and interpret your results.

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#### Solution Preview

a. Find the sample correlation between returns on assets and the ratio of loans to deposits.

r = 0.848

Please refer to the attachment for a full solution.

b. Interpret the intercept and slope of the estimated regression line. ...

#### Solution Summary

This response provides guidelines to calculate a sample correlation, to interpret the intercept of a regression line, and to test a null hypothesis.