Question

An author of a book discusses how statistics can be used to judge both a baseball player’s potential and a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-square regression equation ^y = 2.96x-0.4877.Complete parts (a) thru (d).

A. Interpret the slope. Choose the answer below.

A. For each percentage point increase in on-base percentage, the on-base percentage will increase by 2.96 percentage points, on average.
B. For each percentage point increase in winning percentage, the on-base percentage will increase by 2.96 percentage points, on average.
C. For each percentage point increase in on-base percentage, the on-base percentage will in decrease by 2.96 percentage points, on average.
D. For each percentage point increase in winning percentage, the on-base percentage will in decrease by 2.96 percentage points, on average.

B. For this baseball season, the lowest on-base percentage was 0.320 and the highest on-base percentage was 0.366. Does it make sense to interpret the y-intercept?
___Yes
___No

C. Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage was 0.240?
___No, it would be a bad idea.
___Yes, it would be a good idea.

D. A certain team had an on-base percentage of 0.322 and a winning percentage of 0.544. What is the residual for that team? How would you interpret this residual?

The residual for the team is ___. (Round to four decimal places as needed.)

How would you interpret this residual?
__A. This residual indicates the winning percentage of the team and the on-base percentage of other teams do not vary.
__B. This residual indicates that the winning percentage of the team is above average for the teams with a winning percentage of 0.544.
__C. This residual indicates that the winning percentage of the team is above average for the teams with an on-base percentage of 0.322.
__D. This residual indicates that the winning percentage of the team is below average for the teams with an on-base percentage of 0.322.

Answer 1

A.)

Slope: 2.96

For each percentage point increase in on-base percentage, the winning percentage will increase by 2.96 points, on average.

B.) Yes, it is clear that the values of x are positive. Neither is it 0. It tells the graph does not intercept the y axis.

C.) Yes, we can calculate the predicted value of winning percentage by putting 0.240 in place of x in the regression equation. It will give the predicted winning percentage value to be 0.2227.

D.) The residual for the team is 0.07858.

Part c.) The residual is the vertical distance between a data point and the regression line.

Hence positive sign of the residual indicates that it is above regression line. At the point x=0.322