Question

An analyst believes that the only important determinant of banks' returns on assets $(Y$ ) is the ratio of loans to deposits $(X)$. For a random sample of 20 banks, the sample regression line $$ y=0.97+0.47 x $$ was obtained with coefficient of determination 0.720 . a. Find the sample correlation between returns on assets and the ratio of loans to deposits. b. Test against a two-sided alternative at the $5 \%$ significance level the null hypothesis of no linear association between the returns and the ratio.

   An analyst believes that the only important determinant of banks' returns on assets $(Y$ ) is the ratio of loans to deposits $(X)$. For a random sample of 20 banks, the sample regression line
$$
y=0.97+0.47 x
$$
was obtained with coefficient of determination 0.720 .
a. Find the sample correlation between returns on assets and the ratio of loans to deposits.
b. Test against a two-sided alternative at the $5 \%$ significance level the null hypothesis of no linear association between the returns and the ratio.

Statistics for Business and Economics: Global Edition

Newbold P., Carlson… 8th Edition

Chapter 11, Problem 79

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Step 1

The coefficient of determination, $ R^2 $, is given as 0.720. The sample correlation coefficient $ r $ is the square root of $ R^2 $, and its sign matches the sign of the slope of the regression line. Since the slope $ b = 0.47 $ is positive, $ r $ is Show more…

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An analyst believes that the only important determinant of banks' returns on assets $(Y$ ) is the ratio of loans to deposits $(X)$. For a random sample of 20 banks, the sample regression line $$ y=0.97+0.47 x $$ was obtained with coefficient of determination 0.720 . a. Find the sample correlation between returns on assets and the ratio of loans to deposits. b. Test against a two-sided alternative at the $5 \%$ significance level the null hypothesis of no linear association between the returns and the ratio.

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