Question

Using answers from previous questions, the difference in the predicted scores between the Italian and seafood/steakhouse restaurants, both of which charge a price of $20, is 3.038. This is the same as the coefficient corresponding to the dummy variable for the type of restaurant. Is this result a coincidence or expected?

Answer 1

The observed difference in predicted scores between restaurant types is aligned with regression analysis expectations, illustrating the correct interpretation of the dummy variable coefficient.

Step-by-step explanation:

The difference in the predicted scores between the Italian and seafood/steakhouse restaurants being 3.038, which corresponds to the coefficient of the dummy variable for the type of restaurant, is expected, not a coincidence. The dummy variable is used in regression analysis to represent categorical predictors that have qualitative differences. The coefficient of the dummy variable represents the expected change in the response variable (predicted scores) when changing from the reference category (in this case, probably the Italian restaurant) to the category represented by the dummy (seafood/steakhouse). So, the fact that the difference in predicted scores is equivalent to the coefficient of the dummy variable aligns perfectly with what is expected in regression analysis when comparing two categories at the same price point.