# ch4 - Chapter 4 Linear Regression with One Regressor...

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Chapter 4 Linear Regression with One Regressor

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Question #1: Does Reducing Class Size Improve Elementary School Education? I In many school districts, student performance is measured by standardized tests. I So the question is, "If the class size is reduced, what will the effect be on standardized test scores?" I Or, "If the class size is changed by a certain amount, what would be the expected change in standardized test score?"
The Linear Regression Model Let β ClassSize be the ratio of change in test score to change in class size: β ClassSize = change in TestScore change in ClassSize = Δ TestScore Δ ClassSize . That is the deﬁnition of the slope of a straight line relating test score and class size: TestScore = β 0 + β ClassSize ClassSize , where β 0 is the intercept. There are many other factors inﬂuencing the test scores. But for now, let us lump all the "other factors" together, and write the relationship as: TestScore = β 0 + β ClassSize ClassSize + other factors.

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The Linear Regression Model Suppose you have a sample of n districts. Let Y i be the average test score, let X i be the average class size, and let u i denote the other factors in the i th district: Y i = β 0 + β 1 X i + u i , for i = 1, . .., n , where β 0 is the intercept and β 1 is the slope . This is a linear regression model with a single regressor I Y is the dependent variable, the regressand , or the left-hand variable. I X is the independent variable, the regressor, or the right-hand variable .
The Linear Regression Model The ﬁrst part β 0 + β 1 X i is the population regression line or the population regression function . I This is the relationship that holds between Y and X on average over the population. I The population regression line is the prediction of the dependent variable. β 0 and β 1 are the coefﬁcients (parameters) of the population regression line. I

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## This note was uploaded on 11/20/2011 for the course ECONOMICS 220:322 taught by Professor Otusbo during the Fall '10 term at Rutgers.

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ch4 - Chapter 4 Linear Regression with One Regressor...

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