The least squares estimates are The estimated response of sales to advertising

# The least squares estimates are the estimated

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The least squares estimates are:The estimated response of sales to advertising is:What is the marginal effect of advertising on sales if the advertising expenditure level is \$500?What is the marginal effect of advertising on sales if the advertising expenditure level is \$2000?±2109.727.64012.1512.768se 6.80 1.046 3.556 0.941SALESPRICEADVERTADVERTEq. 5.24Extending the Model for Burger Barn Sales±12.1515.536SALESADVERTADVERT 5.6 Polynomial Equations 5.6.2 Principles of Econometrics, 4t h Edition Page 19 Chapter 5: The Multiple Regression Model 5.6 Polynomial Equations Principles of Econometrics, 4t h Edition Page 22 Chapter 5: The Multiple Regression Model 5.7 Interaction Variables Suppose that we wish to study the effect of income and age on an individual’s expenditure on pizza An initial model would be: Implications of this model are: 1. : For a given level of income, the expected expenditure on pizza changes by the amount β 2 with an additional year of age 2. : For individuals of a given age, an increase in income of \$1,000 increases expected expenditures on pizza by β 3 1 2 3 β β β PIZZA AGE INCOME e Eq. 5.27 2 β E PIZZA AGE 3 β E PIZZA INCOME Interaction Term Principles of Econometrics, 4t h Edition Page 23 Chapter 5: The Multiple Regression Model Table 5.4 Pizza Expenditure Data 5.7 Interaction Variables Principles of Econometrics, 4t h Edition Page 24 Chapter 5: The Multiple Regression Model The estimated model is:The signs of the estimated parameters are as we anticipated: both AGEand INCOMEhave significant coefficients, based on their tstatisticsIs it reasonable to expect that, regardless of the age of the individual, an increase in income by \$1,000 should lead to an increase in pizza expenditure by \$1.83?342.887.5761.832(t) -3.27 3.95PIZZAAGEINCOME - 5.7 Interaction Variables Principles of Econometrics, 4t h Edition Page 25 Chapter 5: The Multiple Regression Model It is more reasonable to assume that as a person grows older, his marginal propensity to spend on pizza declines That is, the effect of income depends on the age of the individual. One way of accounting for such interactions is to include an interaction variable that is the product of the two variables involved. 5.7 Interaction Variables Principles of Econometrics, 4t h Edition Page 26 Chapter 5: The Multiple Regression Model We will add the interaction variable ( AGE × INCOME ) to the regression model The new model is: Implications of this revised model are: 1.  • • • 