a. Regress sales per capita on advertising expenditure per capita, controlling for local income as an interval variable, where intervals are <$35,000, $35,000$44,999, $45,000$54,999, and $55,000+, and <$35,000 is the base group. In the equation below, Income3545 indicates income $35,000$44,999, Income4555 indicates income $45,000$54,999, and Income55 indicates income $55,000+.

SalesPerCapita = ? + ? Income3545 + ? Income4555 + ? Income55 + ? AdvExpPerCap

For the remainder of the question, assume the data-generating process is SalesperCapita_i = + ₁AdExpperCapita_i + ₂Inc35-45_i + ₃Inc45-55_i + ₄Inc55_i + U_i and that all other necessary assumptions toward establishing causality and performing inference hold.

b. Interpret the coefficient for Income4555.

multiple choice 1

• The difference in sales per capita when income goes from below $35,000 to $45,000-$54,999, holding advertising expenditure per capita fixed

• The difference in sales per capita when income goes from below $35,000 to $45,000-$54,999

• The increase in sales per capita when income increases from $45,000-$54,999

• The difference in sales per capita when income goes from $45,000-$54,999 to below $35,000, holding advertising expenditure per capita fixed

c. According to this regression, what is the effect on sales per capita when average local income increases from $35,000$44,999 to $55,000+?

d. At the 95% confidence level, test whether there is evidence of a quadratic relationship between sales per capita and advertising expenditure per capita.

• Accept that there is no quadratic relationship.

• Fail to reject that there is no quadratic relationship.

• Accept that there is a quadratic relationship.

• Reject that there is no quadratic relationship.