Question

an official for a national dog show studies the characteristics of one breed of dog, the dandie dinmont terrier. two common measurements are the height and weight of the dog, and the official would like to develop a model that would be helpful in predicting weight based on a given height. the official first makes a scatterplot that relates height and weight, then another that compares the logs of each measurement. based on the graphs, which type of model is likely appropriate for predicting weight from height? a linear model is appropriate because the graph of the transformed data is roughly linear. a power model is appropriate because the scatterplot of height versus weight appears curved. a power model could be appropriate because the scatterplot of log height versus log weight is roughly linear. the next step is to look at the residual plot. an exponential model is appropriate because the scatterplot of log height versus log weight has a stronger linear relationship than the scatterplot of the non - transformed data.

Explanation:

• A power model has the form \( y = ax^{b}\). Taking the logarithm of both sides gives \(\log y=\log a + b\log x\). If the scatter - plot of \(\log x\) versus \(\log y\) is roughly linear, a power model is appropriate.
• The first option is incorrect because we are not given a graph of transformed data (assuming the first scatter - plot is of non - transformed data).
• The second option is too vague as just saying the scatter - plot is curved does not fully justify the model.
• The fourth option is incorrect because for an exponential model \(y = ab^{x}\), taking the logarithm gives \(\log y=\log a+x\log b\) (linear in \(x\), not in \(\log x\)).

Answer:

A power model could be appropriate because the scatterplot of log height versus log weight is roughly linear. The next step is to look at the residual plot.