Problem 1. Football fans are wondering if a team that is good at defending against rushing will also be good at offensive rushing. Specifically they are asking the question if the number of a team's offensive rushing touchdowns (otd) can be predicted from the number of touchdowns scored against them (dtd). Data was collected from all NFL teams for the 2020 season, it is listed below. Remember to comment on your work for each problem and sub-problem.

team name otd dtd 1 49ers 19 12 2 Bears 12 11 3 Bengals 13 13 4 Bills 16 21 5 Broncos 13 22 6 Browns 21 16 7 Buccaneers 16 10 8 Cardinals 22 13 9 Chargers 12 17 10 Chiefs 13 14 11 Colts 20 16 12 Cowboys 14 20 13 Dolphins 15 17 14 Eagles 16 20 15 Falcons 13 15 16 FootTeam 18 14 17 Giants 13 14 18 Jaguars 9 23 19 Jets 9 16 20 Lions 17 27 21 Packers 16 16 22 Panthers 19 17 23 Patriots 20 17 24 Raiders 20 24 25 Rams 19 12 26 Ravens 24 12 27 Saints 30 11 28 Seahawks 15 18 29 Steelers 12 13 30 Texans 10 24 31 Titans 26 18 32 Vikings 20 19

i) Make a plot of the residuals against the predicted values. Is there evidence that either more terms are needed in the model or that the variance is unequal?

j) How well do you think this result generalizes to other seasons?

problem 2. In general for a simple linear regression model, if the R² value is low (say < .2) does that mean that there is no association between the x and y variables? Briefly explain.

problem 3. In a simple linear regression model, which test is generally more important, the test for the intercept or for the slope? Briefly explain.