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 modely = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + β6x6 + εwhere x3, x4, x5, and x6 are dummy variable values, withx3 = 1 in first quarter of each year, 0 otherwisex4 = 1 in second quarter of each year, 0 otherwisex5 = 1 in third quarter of each year, 0 otherwisex6 = 1 in fourth quarter of each year, 0 otherwiseExplain 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 + εinterpret the coefficients on the dummy variables in the model.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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.
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