# Question: An economist wants to estimate a regression equation relating demand

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 + β6x6 + ε

interpret the coefficients on the dummy variables in the model.

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 + β6x6 + ε

interpret the coefficients on the dummy variables in the model.

**View Solution:**## Answer to relevant Questions

Write brief reports, including examples, explaining the use of each of the following in specifying regression models: a. Dummy variables b. Lagged dependent variables c. The logarithmic transformation The following model was fitted to data from 28 countries in 1989 in order to explain the market value of their debt at that time: y = secondary market price, in dollars, in 1989 of $100 of the country’s debt x1 = 1 if U.S. ...A local public utility would like to be able to predict a dwelling unit's average monthly electricity bill. The company statistician estimated by least squares the following regression model: yt = β0 + β1x1t + β2x2t + ...Jack Wong, a Tokyo investor, is considering plans to develop a primary steel plant in Japan. After reviewing the initial design proposal, he is concerned about the proposed mix of capital and labor. He has asked you to ...Health care cost is an increasingly important part of the U.S. economy. In this exercise you are to identify variables that are predictors for hospital cost, either individually or in combination. Use the data file Health ...Post your question