An economist wants to estimate a regression equation relating demand for a product (Y) to its price (X 1 ) and income (X 2 ). It is to be based on 12 years of quarterly data. However, it is known that...

An economist wants to estimate a regression equation relating demand for a product (Y) to its price (X₁) and income (X₂). It is to be based on 12 years of quarterly data. However, it is known that demand for this product is seasonal; that is, it is higher at certain times of the year than others.
a. One possibility for accounting for seasonality is to estimate the model
y = β₀
+ β₁x₁
+ β₂x₂
+ β₃x₃
+ β₄x₄
+ β₅x₅
+ β₆x₆
+ ε
where x₃, x₄, x₅, and x₆
are dummy variable values, with
x₃
= 1 in first quarter of each year, 0 otherwise
x₄
= 1 in second quarter of each year, 0 otherwise
x₅
= 1 in third quarter of each year, 0 otherwise
x₆
= 1 in fourth quarter of each year, 0 otherwise
Explain why this model cannot be estimated by least squares.
b. For a model that can be estimated is as follows:
y = β₀
+ β₁x₁
+ β₂x₂
+ β₃x₃
+ β₄x₄
+ β₅x₅
+ ε
interpret the coefficients on the dummy variables in the model.