Question

Suppose we are interested in motor vehicle thefts (from a research standpoint). We collect data on vehicle thefts by state and regress that data on state population (in millions), as well as dummy variables for the region in which the state is located. In the year this data was collected, Idaho's population was 1.8 million. What do you predict the number of thefts are for Idaho? If the actual number of thefts in Idaho was 1,767, what is the residual for Idaho and what does this tell us?

Answer 1

To predict Idaho's vehicle thefts and find the residual, we would use a regression model that is not provided. The residual is the difference between actual thefts (1,767) and predicted thefts, indicating our model's accuracy.

Step-by-step explanation:

The question involves using a regression model to predict motor vehicle thefts based on state population and regional dummy variables. To predict the number of thefts for Idaho with a population of 1.8 million, one would need the estimated coefficients from such a model; however, since we don't have the output of the regression model, an exact number can't be provided. Assuming a model has been run and a prediction made, the residual for Idaho would be the difference between the actual number of thefts (1,767) and the predicted number of thefts. The residual tells us how far off our model's prediction was from the actual observed value.

A positive residual indicates that the actual number of thefts was higher than predicted, while a negative residual means the model overestimated the thefts. The residual can provide insights into the factors not accounted for by the model and it can help in refining the model for better future predictions.