91Ó°ÊÓ

The relation between y (number of points scored in each Super Bowl from 1980) and x (years starting from 1980 and coded as 1,2,3…..) is modeled by 5 different models. The \({R^2}\) value of each model is provided.

To determine which of the 5 models is the best fit for the given two variables, the model with the highest value of\({R^2}\)is considered the most appropriate.

The following are the\({R^2}\)values corresponding to the 5 models:

• Linear:\({R^2} = 0.147\)
• Quadratic:\({R^2} = 0.255\)
• Logarithmic:\({R^2} = 0.176\)
• Exponential:\({R^2} = 0.175\)
• Power:\({R^2} = 0.203\)

The highest value of\({R^2}\)is equal to 0.255 and corresponds to the quadratic model.

Thus, it can be concluded that the quadratic model is the best.

For a fitted model to be good, the value of\({R^2}\)should be substantially large.

Here, the value of\({R^2}\)corresponding to the quadratic model is very low, equal to 0.255.

Thus, the fitted quadratic model is not a good model.

Since the model is not a good model, the predicted values obtained from this model are not accurate.

Thus, it is not advisable to use the quadratic model to predict the number of points scored in a future Super Bowl game.