Question

A homeowner notices that the electric bill for the house is often much higher in the summer months. 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.
B. Logarithmic model is appropriate because logarithms were used to transform the data sets.
C. Power model is appropriate because the scatterplot of log temperature and log bill is roughly linear, and the residual plot shows no distinct pattern.
D. Exponential model is appropriate because the scatterplot of log temperature and log bill is roughly linear.

Answer 1

The most suitable model for modeling electric bills based on mean monthly temperature is the power model. Option C is correct.

Step-by-step explanation:

To ascertain the most fitting model for predicting electric bills based on mean monthly temperature, a comprehensive analysis of both the scatterplot and residual plot is imperative. In this context, option C, the Power model, emerges as the most suitable choice. The decision is grounded in the examination of the scatterplot depicting the relationship between log-transformed temperature and log-transformed bill amounts. Notably, the scatterplot exhibits a discernibly linear pattern, which is indicative of the appropriateness of a Power model.

The decision to opt for a Power model is further reinforced by scrutinizing the residual plot. A crucial aspect of model selection lies in assessing the residuals—deviations between the predicted and actual values. In this case, the residual plot does not reveal any discernible pattern, suggesting that the Power model adequately captures the variance in the data without systematic errors or biases.

In essence, the choice of the Power model is driven by the visual alignment of the scatterplot with linearity, and the absence of conspicuous patterns in the residual plot reinforces the model's appropriateness. This careful analysis ensures that the selected model is not only statistically sound but also aligns well with the inherent characteristics of the data, enhancing its predictive capabilities for estimating electric bills based on mean monthly temperature.