President Obama€™s statewide approval ratings and Democratic candidates€™ shares of votes in Senate races in 2010 and 2012 are compared in Table 65 for 12 randomly selected Senate races in recent years.

Let P be President Obama€™s statewide approval rating (in per- cent) and D be a Democratic candidate€™s share of votes (in percent) in a Senate race, both for the same state.
a. Construct a scatterplot by hand. Assume P is the explanatory variable.
b. Describe the four characteristics of the association. Compute and interpret r as part of your analysis.
c. Draw a linear model on your scatterplot.
d. President Obama€™s approval rating in March 2014 was 33% in South Dakota, which had one Democratic senator: Tim Johnson. Assuming Senator Johnson ran for reelection in 2014 and President Obama€™s approval rating didn€™t change, use your model to predict Senator Johnson€™s share of votes. On the basis of your result, explain why his seat was viewed to be at risk.
e. Did you perform interpolation or extrapolation in part (d)? Do you have much faith in your result? Explain.

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Table 65 President Obama's Statewide Approval Ratings versus Democratic Candidates' Shares of Votes in Senate Races President Obama's Statewide Approval Rating percent) 42 51 56 40 46 Democratic Candidate's Share of Votes in a Senate Race percent) 34 48 48 37 53 48 41 75 71 59