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.