{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Econ 281 - Regression Analysis with One Variable UP_1

# Econ 281 - Regression Analysis with One Variable UP_1 - 1...

This preview shows pages 1–12. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Regression Analysis with One Variable Introduction to Econometrics (18) Econ 281 Spring Quarter 2007 2 Introduction • Remember our two examples – Student Test Scores and Student-Teacher Ration – Wages and Education • Both are Relationships between two variables – Dependent Variable: Test Scores, Wage – Independent Variable (Regressors): Student-Teacher Ration, Education • Simple Regression Analysis is all about investigating the relationship between those two variables 3 Introduction • We start out by “looking” at the population relationship between the two variables – Note: We are not really able to do that • The population regression function: • m(x i ) is a general function • Example: ( 29 ( 29 i i i x m x X Y E = = | ( 29 ( 29 i i i edu m edu Education wage E = = | 4 Introduction • We will simplify things by assuming that m(x i ) is linear • Note: It is important to remember that this is an assumption and that we NEVER actually observe the TRUE relationship between those variables i i X x m ⋅ + = 1 ) ( β β 5 Introduction • Now we “confront” this model with sample data taken from the population. • Would we expect the above relationship to hold perfectly? • No! – Data differs because other variables influence Y i – Data differs because of random variation i i X Y ⋅ + = 1 β β 6 Introduction • Solution: We add an ERROR TERM (u i ) to the equation • The error term captures – the effect of other variables – random deviations from Y i • This gives us the linear regression model i i i u X Y + ⋅ + = 1 β β 7 The Linear Regression Model i i i u X Y + ⋅ + = 1 β β Slope Coefficient Intercept Coefficient Dependent Variable Independent Variable (Regressor) Error Term 8 (X 1 ,Y 1 ) 600 620 640 660 680 700 15 20 25 Test Scores and Student-Teacher Ratio Student-Teacher Ratio Test Scores (Unobserved) Population Regression Function =u 1 (X 2 ,Y 2 ) (X 3 ,Y 3 ) =u 2 =u 3 9 Interpretation of the Coefficients • Lets look at the Test Score example – Where TestScore = Average Test Score of a class – STR = Student-Teacher Ration of class • Knowledge of the slope coefficient would enable us to predict the effect on Test Scores of an change in the Class Size STR ⋅ + = 1 TestScore β β STR ∆ ∆ = = TSC Ratio acher Student/Te in change Score Test in change 1 β 10 Interpretation of the Coefficients • Assume the student-teacher ratio changes • Then we can calculate the predicted change in Test Scores according to • If we know both the intercept AND the slope coefficient we can also predict the average test score (and the change) for a school district tio StuTeachRa ∆ ⋅ = ∆ 1 TestScore β tio StuTeachRa ⋅ + = 1 TestScore β β 11 The Linear Regression Model • Note that is the POPULATION regression function!!...
View Full Document

{[ snackBarMessage ]}

### Page1 / 49

Econ 281 - Regression Analysis with One Variable UP_1 - 1...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online