Question

10. Suppose that for a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least squares regression equation: ?̂ = 2.94? − 0.4875. For this baseball season, the lowest on-base percentage was 0.310 and the highest was 0.362. a. Underline the correct choice and fill in the blank in the following statement: As the on-base percentage increases by 5 percent, the predicted winning percentage increases / decreases by__________ b. Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage is 0.156? Why or why not? c. Based on this model, what would you expect the winning percentage to be for a team with on-base percentage 0.350?

Answer 1

Answer:-

Given That:-

Suppose that for a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least squares regression equation:

Given,

?̂ = 2.94? − 0.4875.

a. Underline the correct choice and fill in the blank in the following statement: As the on-base percentage increases by 5 percent, the predicted winning percentage increases / decreases by__________

= 2.94x - 0.4875

= 2.94(5) - 0.4875

= 14.7 - 0.4875

As the on-base percentage increased by 5 percent, the predicted winning percentage increases by 14.7%

b. Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage is 0.156? Why or why not?

Not a good idea, beacuse this would be an extrapolation and X-value of 0.156 is well outside of the range of values the regression equation was based upon.

c. Based on this model, what would you expect the winning percentage to be for a team with on-base percentage 0.350?

= 2.94x - 0.4875

= 2.94(0.350) - 0.4875

= 0.5415

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