Question

a homeowner notices that the electric bill for the house is often much higher in the summer months. collecting data from the last 18 monthly electric bills, the amount of each bill is plotted against the mean temperature for each month. the logs of both the mean monthly temperature and the electric bill are taken in order to develop a linear model. log(bill) vs. log(temperature) scatterplot of log(bill) vs. log(temperature) shown based on the scatterplot and residual plot, which type of model is most suitable for modeling electric bills based on mean monthly temperature? a linear model is appropriate because the residual plot shows a random scatter. a logarithmic model is appropriate because logarithms were used to transform the data sets. a power model is appropriate because the scatterplot of log temperature and log bill is roughly linear, and the residual plot shows no distinct pattern. an exponential model is appropriate because the scatterplot of log temperature and log bill is roughly linear.

Explanation:

A power model is suitable when log-transforming both variables results in a linear scatterplot, as this indicates the original variables follow a power relationship ($\text{Bill} = k \cdot \text{Temperature}^n$ for constants $k,n$). The residual plot showing no pattern confirms the appropriateness of the model.

Answer:

C. A power model is appropriate because the scatterplot of log temperature and log bill is roughly linear, and the residual plot shows no distinct pattern.