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# Interpreting a Multiple Regression with a Quadratic

EMETRC-YS19JD

Suppose you estimate a linear regression model of ticket sales ($S$) as a function of consumers' income ($I$) in \$1,000, income squared ($I^2$), and price of the ticket ($P$): $$S = \beta_0 + \beta_1 I + \beta_2 I^2 + \beta_3 P + \varepsilon$$ What is the marginal impact of an increase in income on ticket sales? A$\beta_1$B$\beta_2$C$\beta_1 + 2\beta_2 I$D$\beta_1 + \beta_2 I\$