4. The data set CA3_RainGrad.csv contains data on rainfall and percentage graduating from high
school in all 50 US states, plus the District of Columbia. You may use R for this question.
(a) Generate a scatter plot of HDGrad versus Rain.
(b) Estimate Pearson's correlation, Spearman's rank correlation, and Kendall's tau for these data
and perform appropriate two-sided hypothesis tests for each. State clearly the null and alter-
native hypotheses as well as your conclusions in each case.
Note: you may assume the variables are jointly bivariate normal when testing Pearson's cor-
relation and you can rely on R's output \textendash{} without performing permutation tests \textendash{} for the
other two measures of association.
(c) Briefly discuss the statement 'correlation does not imply causation' in the context of these data.
(d) Let $r$ and $r_s$ denote Pearson's and Spearman's correlation coefficients, respectively. Obtain
these values in R and use them to verify by hand the values of the associated test statistics $t$
and $S$. Show your workings.
