Question

91. Putting success How well do professional golfers putt from different distances? Researchers collected data on the percent of putts made for various distances to the hole (in feet). 48 Here is linear regression output for three different models, along with a residual plot for each model. Model 1 is based on the original data, while Models 2 and 3 involve transformations of the original data. Model 1. Percent made vs. Distance Predictor Coef SE Coef T P Constant 83.6081 4.7206 17.711 0.0000 Distance -4.0888 0.3842 -10.64 0.0000 S = 9.17 R-sq = 0.870 R-sq(adj) = 0.862 Model 2. ln(percent made) vs. ln(distance) Predictor Coef SE Coef T P Constant 5.5047 0.1628 33.821 0.0000 ln(distance) -0.9154 0.0702 -13.04 0.0000 S = 0.196 R-sq = 0.909 R-sq(adj) = 0.904 Model 3. ln(percent made) vs. Distance Predictor Coef SE Coef T P Constant 4.6649 0.0825 56.511 0.0000 Distance -0.1091 0.0067 -16.24 0.0000 S = 0.160 R-sq = 0.939 R-sq(adj) = 0.936 a. Which model does the best job of summarizing the relationship between distance and percent made? Explain your reasoning. b. Using the model chosen in part (a), calculate and interpret the residual for the point where the golfers made 31% of putts from 14 feet away.

          91. Putting success How well do professional golfers putt from different distances? Researchers collected data on the percent of putts made for various distances to the hole (in feet). 48

Here is linear regression output for three different models, along with a residual plot for each model. Model 1 is based on the original data, while Models 2 and 3 involve transformations of the original data.

Model 1. Percent made vs. Distance
Predictor Coef SE Coef T P
Constant 83.6081 4.7206 17.711 0.0000
Distance -4.0888 0.3842 -10.64 0.0000
S = 9.17 R-sq = 0.870 R-sq(adj) = 0.862

Model 2. ln(percent made) vs. ln(distance)
Predictor Coef SE Coef T P
Constant 5.5047 0.1628 33.821 0.0000
ln(distance) -0.9154 0.0702 -13.04 0.0000
S = 0.196 R-sq = 0.909 R-sq(adj) = 0.904

Model 3. ln(percent made) vs. Distance
Predictor Coef SE Coef T P
Constant 4.6649 0.0825 56.511 0.0000
Distance -0.1091 0.0067 -16.24 0.0000
S = 0.160 R-sq = 0.939 R-sq(adj) = 0.936

a. Which model does the best job of summarizing the relationship between distance and percent made? Explain your reasoning.

b. Using the model chosen in part (a), calculate and interpret the residual for the point where the golfers made 31% of putts from 14 feet away.

91. Putting success How well do professional golfers putt from different distances? Researchers collected data on the percent of putts made for various distances to the hole (in feet). 48

Here is linear regression output for three different models, along with a residual plot for each model. Model 1 is based on the original data, while Models 2 and 3 involve transformations of the original data.

Model 1. Percent made vs. Distance
Predictor Coef SE Coef T P
Constant 83.6081 4.7206 17.711 0.0000
Distance -4.0888 0.3842 -10.64 0.0000
S = 9.17 R-sq = 0.870 R-sq(adj) = 0.862

Model 2. ln(percent made) vs. ln(distance)
Predictor Coef SE Coef T P
Constant 5.5047 0.1628 33.821 0.0000
ln(distance) -0.9154 0.0702 -13.04 0.0000
S = 0.196 R-sq = 0.909 R-sq(adj) = 0.904

Model 3. ln(percent made) vs. Distance
Predictor Coef SE Coef T P
Constant 4.6649 0.0825 56.511 0.0000
Distance -0.1091 0.0067 -16.24 0.0000
S = 0.160 R-sq = 0.939 R-sq(adj) = 0.936

a. Which model does the best job of summarizing the relationship between distance and percent made? Explain your reasoning.

b. Using the model chosen in part (a), calculate and interpret the residual for the point where the golfers made 31% of putts from 14 feet away.

Added by Timothy L.

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