Answer the following question about quantitative analysis:

(part a)

Suppose you estimate a regression model predicting the amount of money spent on ice cream. The main independent variable is income. A test for a linear relationship indicates that the slope coefficient on income is statistically significant at the 5% significance level. Why would it be inappropriate to say that you "proved" that higher income leads to more ice cream sales?

(part b)

Consider the study on ice cream sales and income. Provide an example of another independent variable that could lead to interaction effects on ice cream sales with income. Discuss what your interaction term would be and why it would be appropriate.