One of the problems when estimating the size of animal populations from aerial surveys is that animals may bunch together, making it difficult to distinguish and count them accurately. For example, a horse standing alone is easy to spot; if seven horses huddled close together some may be missed, resulting in an undercount. The relative frequency of undercounts is typically reported as a percent. For example, if there are 10 horses in a group, a person in the plane may typically count fewer than 10 horses 20% of the time. In a recent study, the percent of sightings that resulted in an undercount was related to the size of the "group" of horses and donkeys; the following data were gathered: After fitting a straight line model, , significant curvature was detected in the residual plot, and two nonlinear models were chosen for further analysis, the exponential and the power models. The computer output for these models is given below, and the residual plots follow. Residual Plots
a) For the exponential model, calculate the predicted log (%undercount) for a group size = 10.
b) Use your calculations from part (a) to predict the %undercount for a group size = 10.
c) Generally speaking, which of the two models, power or exponential, is better at predicting the log (Percent Undercount)? Provide statistical justification for your choice.

Question

One of the problems when estimating the size of animal populations from aerial surveys is that animals may bunch together, making it difficult to distinguish and count them accurately. For example, a horse standing alone is easy to spot; if seven horses huddled close together some may be missed, resulting in an undercount. The relative frequency of undercounts is typically reported as a percent. For example, if there are 10 horses in a group, a person in the plane may typically count fewer than 10 horses 20% of the time. In a recent study, the percent of sightings that resulted in an undercount was related to the size of the "group" of horses and donkeys; the following data were gathered:  After fitting a straight line model,  , significant curvature was detected in the residual plot, and two nonlinear models were chosen for further analysis, the exponential and the power models. The computer output for these models is given below, and the residual plots follow.  Residual Plots     
a) For the exponential model, calculate the predicted log (%undercount) for a group size = 10. 
b) Use your calculations from part (a) to predict the %undercount for a group size = 10. 
c) Generally speaking, which of the two models, power or exponential, is better at predicting the log (Percent Undercount)? Provide statistical justification for your choice.

Quizplus · Accepted Answer

The Answer of One of the problems when estimating the size of animal populations from aerial surveys is that animals may bunch together, making it difficult to distinguish and count them accurately. For example, a horse standing alone is easy to spot; if seven horses huddled close together some may be missed, resulting in an undercount. The relative frequency of undercounts is typically reported as a percent. For example, if there are 10 horses in a group, a person in the plane may typically count fewer than 10 horses 20% of the time. In a recent study, the percent of sightings that resulted in an undercount was related to the size of the "group" of horses and donkeys; the following data were gathered:  After fitting a straight line model,  , significant curvature was detected in the residual plot, and two nonlinear models were chosen for further analysis, the exponential and the power models. The computer output for these models is given below, and the residual plots follow.  Residual Plots     
a) For the exponential model, calculate the predicted log (%undercount) for a group size = 10. 
b) Use your calculations from part (a) to predict the %undercount for a group size = 10. 
c) Generally speaking, which of the two models, power or exponential, is better at predicting the log (Percent Undercount)? Provide statistical justification for your choice.

One of the Problems When Estimating the Size of Animal