In the 2014 election, Republicans took control of the Senate. A major theme during each senator's campaign was the popularity of President Obama (a Democrat). The scatter diagram below shows the presidential approval rating (percent of registered voters who approve of the job the president is doing) versus the percentage of votes received by the Republican senatorial candidate in the 2014 election.

(a) What type of relation appears to exist between presidential approval ratings and percentage of Republican votes?
(b) There are 32 observations in the data set (Alabama was an uncontested election). The correlation between presidential approval and percent Republican is -0.795. Does this suggest a linear relation exists between presidential approval and percent Republican?
(c) The least-squares regression line treating presidential approval, x, as the explanatory variable and percent Republican as the response variable, y, is ŷ = -0.7059x + 78.95. Interpret the slope. What does this say about candidates of the same party as the president running in Senate elections?
(d) If President Obama's approval rating was 50%, what would you expect the percent of votes for the Republican candidate to be?
(e) In North Carolina, Pat Tillis (a Republican) won the election with 49% of the vote where President Obama's approval rating was 43%. Did Tillis get a higher percent of the votes than would be expected for this presidential approval rating?