re interested in studying cigarette demand by young adults. Lets consider the following model: ncaj = β0 + β1price + β2age + β3income + u where ncaj is monthly cigarette consumption in packs, price is the price of a pack of cigarettes in dollars, age is age in years, and income is annual income in thousands of dollars.   Consider now an extension of the model  that allow the effect of the price to differ by age. Holding all other factors fixed, is the effect of price on ncaj constant? (This part is theoretical and you do not have to estimate the model.)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
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We are interested in studying cigarette demand by young adults. Lets consider the
following model:
ncaj = β0 + β1price + β2age + β3income + u
where ncaj is monthly cigarette consumption in packs, price is the price of a pack of
cigarettes in dollars, age is age in years, and income is annual income in thousands
of dollars.

 

Consider now an extension of the model  that allow the effect of the
price to differ by age. Holding all other factors fixed, is the effect of price on
ncaj constant? (This part is theoretical and you do not have to estimate the
model.) 

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Just to be clear, could we say that there is a correlation between both values? And that when this happens there are biased estimators rather than unbiased ones so that the third assumption of the multiple linear regression , which is conditional mean expectation does not hold?

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