chapter11

chapter11 - Multiple Linear Regression Response Variable Y...

This preview shows pages 1–6. Sign up to view the full content.

Multiple Linear Regression Response Variable: Y • Explanatory Variables: X 1 ,..., X k Model (Extension of Simple Regression): E ( Y ) = α + β 1 X 1 + + k X k V ( Y ) = σ 2 • Partial Regression Coefficients ( i ): Effect of increasing X i by 1 unit, holding all other predictors constant. Computer packages fit models, hand calculations very tedious

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

View Full Document
Prediction Equation & Residuals • Model Parameters: α, β 1 ,…, β k , σ • Estimators: a , b 1 , …, b k , Least squares prediction equation: Residuals: Error Sum of Squares: Estimated conditional standard deviation: ^ k k X b X b a Y + + + = 1 1 ^ ^ Y Y e - = - = = 2 ^ 2 ) ( Y Y e SSE 1 ^ - - = k n SSE
Commonly Used Plots Scatterplot : Bivariate plot of pairs of variables. Do not adjust for other variables. Some software packages plot a matrix of plots Conditional Plot (Coplot) : Plot of Y versus a predictor variable, seperately for certain ranges of a second predictor variable. Can show whether a relationship between Y and X 1 is the same across levels of X 2 Partial Regression (Added-Variable) Plot : Plots residuals from regression models to determine association between Y and X 2 , after removing effect of X 1 (residuals from ( Y , X 1 ) vs ( X 2 , X 1 ))

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

View Full Document
Example - Airfares 2002Q4 Response Variable: Average Fare ( Y , in \$) Explanatory Variables: – Distance ( X 1 , in miles) – Average weekly passengers ( X 2 ) Data: 1000 city pairs for 4th Quarter 2002 Source: U.S. DOT Descriptive Statistics 1000 50.52 401.23 163.3754 55.36547 1000 108.00 2724.00 1056.9730 643.20325 1000 181.41 8950.76 672.2791 766.51925 1000 AVEFARE DISTANCE AVEPASS Valid N (listwise) N Minimum Maximum Mean Std. Deviation
Example - Airfares 2002Q4 avefare distance avepass 0 200 400 0 200 400 0 1000 2000 3000 0 1000 2000 3000 0 5000 10000 0 5000 10000 Scatterplot Matrix of Average Fare, Distance, and Average Passengers (produced by STATA):

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.

{[ snackBarMessage ]}

Page1 / 17

chapter11 - Multiple Linear Regression Response Variable Y...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online