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Get Full Access to Elementary Statistics - 12 Edition - Chapter 10.6 - Problem 3bsc
Get Full Access to Elementary Statistics - 12 Edition - Chapter 10.6 - Problem 3bsc

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BSC Interpreting R2In Exercise, the quadratic model

ISBN: 9780321836960 18

Solution for problem 3BSC Chapter 10.6

Elementary Statistics | 12th Edition

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Problem 3BSC

BSC Interpreting ?R?2?In Exercise, the quadratic model results in ?R?2?=?0.103. 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.) What does the result suggest about the usefulness of the quadratic model? Exercise Super Bowl and?R2?Let?x?represent years coded as 1, 2, 3, . . . for years starting in 1980, and let ?y? represent the numbers 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: 0.0185; quadratic: 0.103; logarithmic: 0.000557; exponential: 0.0253; power: 0.00264. 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? Example Example 1

Step-by-Step Solution:

Solution 3 BSC Step 1: Let X represents the years coded as 1,2,3,... and Y represents the number of points scored in each super bowl from 1980. Coefficient of determination which measures the variation in Y variable corresponding to the X variable. The Quadratic model (0.103) is the best model compared to other models. Almost 10.30% of the variation in the number of points scored in the super bowl from 1980. This model is better model but it is not the best. When the value of R is close to 1 then the model will be best and the value is closed to zero then it is poor model. The value of the quadratic model is 0.103. Is closed to zero so it cannot be taken as the best model.

Step 2 of 1