Question

A new town was incorporated in 1960. The size of the town's population was recorded every 5 years after 1960. Using the variables x, for number of years since 1960, and y, for the size of the population, three models were created to predict the population from the number of years since 1960.

Model I predicts y from x.
Model II predicts ln(y), the natural logarithm of y, from x.
Model III predicts ln(y) from ln(x).
The following graphs show the residual plot for each model.
Which of the following statements is the best interpretation of the residual plots?
1) The residual plot for Model I shows a random pattern, indicating that the model is a good fit for the data.
2) The residual plot for Model I shows a systematic pattern, indicating that the model is not a good fit for the data.
3) The residual plot for Model II shows a random pattern, indicating that the model is a good fit for the data.
4) The residual plot for Model II shows a systematic pattern, indicating that the model is not a good fit for the data.
5) The residual plot for Model III shows a random pattern, indicating that the model is a good fit for the data.
6) The residual plot for Model III shows a systematic pattern, indicating that the model is not a good fit for the data.

Answer 1

The best interpretation of the residual plots can be determined by analyzing the patterns in each plot. For Model I, a random pattern indicates a good fit, while a systematic pattern indicates a poor fit. The same applies for Model II and Model III.

Step-by-step explanation:

The best interpretation of the residual plots can be determined by analyzing the patterns in each plot. Model I predicts y from x, and if the residual plot for Model I shows a random pattern, it indicates that the model is a good fit for the data. On the other hand, if the residual plot for Model I shows a systematic pattern, it indicates that the model is not a good fit for the data.

Similarly, for Model II, which predicts ln(y) from x, if the residual plot shows a random pattern, it indicates a good fit for the data. However, if the plot shows a systematic pattern, it indicates that the model is not a good fit.

Lastly, for Model III, which predicts ln(y) from ln(x), if the residual plot shows a random pattern, it indicates a good fit for the data. Conversely, if the plot shows a systematic pattern, it indicates that the model is not a good fit.