Chapter 10.5, Problem 3BSC

Super Bowl and R² Let x represent years coded as 1, 2, 3,... for years starting in 1980, and let y represent the number, of points scored in each Super Bowl from 1980. Using the data from 1980 to the last Super Bowl at the time of this writing, we obtain the following values of R² for the different models: linear: 0.147; quadratic: 0.255; logarithmic: 0.176; exponential: 0.175; power 0.203. Based on these results, which model is best? Is the best model a good model? What do the results suggest about predicting the number of points scored in a future Super Bowl game?

3. Interpreting R² In Exercise 2, the quadratic model results in R² = 0.255. Identify the percentage of the variation in Super Bowl points that can be explained by the quadratic model relating the variable of year and the variable of points scored. (Hint: See Example 2.) What does the result suggest about the usefulness of the quadratic model?