1. The Simple Linear Regression Model
RESUME FROM HILL, GRIFFITHS, AND LIM
Principles of Econometrics (2011)
The Simple Linear Regression Model
Al Muizzuddin Fazaalloh, SE., ME.
Universitas Brawijaya

2. An Economic Model
In order to develop the ideas of regression models we are going to use a simple, but important, economic example.
Suppose that we are interested in studying the relationship between household income and expenditure on food.
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3. Cont’d
For the present, suppose that we are interested only in households with an income of $1,000 per week. In this experiment we randomly select a number of households from this population and interview them. We ask the question, ‘‘How much did you spend per person on food last week?’’ Weekly food expenditure, which we denote as y, is a random variable since the value is unknown to us until a household is selected and the question is asked and answered.
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The continuous random variable y has a probability density function (which we will abbreviate as pdf) that describes the probabilities of obtaining various food expenditure values.
The pdf f (y) describes how expenditures are ‘‘distributed’’ over the population and might look like Figure 2.1. The pdf f (y) describes how expenditures are ‘‘distributed’’ over the population and might look like Figure 2.1.
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In order to investigate the relationship between expenditure and incomewe must build an economic model and then a corresponding econometric model that forms the basis for a quantitative or empirical economic analysis.
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7. Cont’d
In most economics textbooks ‘‘consumption’’ or ‘‘expenditure’’ functions relating consumption to income are depicted as linear relationships
The mathematical representation of our economic model of household food expenditure, depicted in Figure 2.2, is
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8. Cont’d
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9. The conditional mean E(y/x) in (2
The conditional mean E(y/x) in (2.1) is called a simple regression function. It is called simple regression not because it is easy, but because there is only one explanatory variable on the right-hand side of the equation.
The unknown regression parameters b1 and b2 are the intercept and slope of the regression function, respectively.
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10. An Econometric Model
The model describes economic behavior, but it is an abstraction from reality
In Figure 2.3 we arrange bell-shaped figures like Figure 2.1, depicting the pdfs of food expenditure f (y/x), along the regression line for each level of income.
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In order to make the econometric model complete we have to make some assumptions
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15. INTRODUCING THE ERROR TERM
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18. Estimating the Regression Parameters
THE LEAST SQUARES PRINCIPLE
To estimate b1 and b2 we want a rule, or formula, that tells us how to make use of the sample observations. Many rules are possible, but the one that we will use is based on the least squares principle.
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