A Financial Economist Wants to Evaluate How Interest Rates Affect $(x)$

Essay

A financial economist wants to evaluate how interest rates affect the inflation rate. Here are some results on yearly prime interest rates $(x)$ and inflation rates $(y)$ for the 13 years 1965 through 1977. $\sum x y=500, \sum y=78$ , $\sum x^{2}=450, \sum y^{2}=600, \sum x=65$ .
For the situation above:
a. Calculate the sample coefficient of determination and correlation coefficient.
b. Give the proportion of variation explained by the regression line.
c. Test the null hypothesis of no correlation against a two-tailed alternative at the 0.01 significance level.