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 + 0.47x
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.