Refer to the data in Exercise 41. First compute a new variable by subtracting points scored

Question:

Refer to the data in Exercise 41. First compute a new variable by subtracting “points scored” – “points allowed.” Call this new variable “point differential.” For the following questions, “wins” will be the dependent variable and “point differential” will be the independent variable. Note that during the National Football League season, each team plays 16 games.

a. Create a scatterplot of “wins” versus “point differential.” What do you observe?

b. Calculate the correlation coefficient for “wins” and “point differential”. Interpret the result.

c. Complete a regression analysis of the relationship. Report and interpret the coefficient of determination.

d. Write the regression equation that predicts “wins.”

e. What is the “point differential” that corresponds with a team that wins 8 games (and loses 8 games)? Interpret this finding.

f. Using the slope of the regression line, in a season, what is the increase in the point differential that corresponds to an increase of one win?

Data From Exercise 41:

For each of the 32 National Football League teams, the numbers of points scored and allowed during the 2018 season are shown here:

Points Points Points Points Team Wins Scored Allowed Team Wins Scored Allowed New York Jets 4 333 441 Chicago Bears 12 421 283 Cleveland Browns 7 359 392 Philadelphia Eagles 367 348 Denver Broncos 329 349 Tennessee Titans 9. 310 303 Jacksonville Jaguars Minnesota Vikings 245 316 Kansas City Chiefs