Question

When using the numbers of points scored in each Super Bowl from 1980 to the last Super Bowl at the time that this exercise was​ written, we obtain the following values of R2 for the different​ models: ​ linear: 0.002;​ quadratic: 0.082;​ logarithmic: 0.003;​ exponential: 0.005;​ power: 0.001. Based on these​ results, which model is​ best? Is the best model a good​ model? Explain.

Answer 1

The best model is the quadratic.

Although is the best model (higher R2), its value of R2 is too low to be considered useful for analysis or prediction.

Explanation:

The best model will be the one that has a higher R2 (goodness-of-fit). This is because the R2 coefficient reflects the how the model fit the real data. R2 will range from 0 to 1 (or 0% to 100%). A value of R2 close to 1 is almost perfect fit and a value of 0 will show no fit at all.

The "best" model (higher R2) is the quadratic model, with R2=0.082.

Although it is the higher value, it is a too low value of R2 to be consider a good model of the real data. This value of R2 shows that only 8.2% of the real data is explained by the model, and it is obviously not enough.