1 / 12

Introduction to Regression Analysis

Introduction to Regression Analysis. Straight lines, fitted values, residual values, sums of squares, relation to the analysis of variance. Population characteristics. Expected value Is a conditional mean: it is dependent on The conditional mean is called the regression

ninon
Download Presentation

Introduction to Regression Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Regression Analysis Straight lines, fitted values, residual values, sums of squares, relation to the analysis of variance

  2. Population characteristics • Expected value • Is a conditional mean: it is dependent on • The conditional mean is called the regression • When this mean is a straight line, we write

  3. Alternately

  4. The Errors • Are independent • This assumption is important • Excluded: Longitudinal data; repeated measures; split units; cross overs; clustering

  5. The sample gives the estimates of the population characteristics • For example: • Some books write: • Your choice (but be clear!)

  6. A simple example • X Y • 1 2 • 2 3 • 3 3 • 4 7 • 5 10

  7. Residual Sum of Squares • Without X: • With X: • The difference is the sum of squares ‘attributable’ to X: The Regression SS

  8. Analysis of variance table • Source SS df MS • Regression 40 1 40 • Residual 6 3 2 • Total 46 4 • F = 40/2 = 20 cf F(1,3) • p-value = P(F > 20) = 0.0208

  9. Regression analysis • . regr y x • Source | SS df MS Number of obs = 5 • -------------+------------------------------ F( 1, 3) = 20.00 • Model | 40 1 40 Prob > F = 0.0208 • Residual | 6 3 2 R-squared = 0.8696 • -------------+------------------------------ Adj R-squared = 0.8261 • Total | 46 4 11.5 Root MSE = 1.4142 • ------------------------------------------------------------------------------ • y | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • x | 2 .4472136 4.47 0.021 .5767667 3.423233 • _cons | -1 1.48324 -0.67 0.548 -5.720331 3.720331 • ------------------------------------------------------------------------------

  10. Centering • . gen xc=x-3 • . regr y xc • Source | SS df MS Number of obs = 5 • -------------+------------------------------ F( 1, 3) = 20.00 • Model | 40 1 40 Prob > F = 0.0208 • Residual | 6 3 2 R-squared = 0.8696 • -------------+------------------------------ Adj R-squared = 0.8261 • Total | 46 4 11.5 Root MSE = 1.4142 • ------------------------------------------------------------------------------ • y | Coef. Std. Err. t P>|t| [95% Conf. Interval] • -------------+---------------------------------------------------------------- • xc | 2 .4472136 4.47 0.021 .5767667 3.423233 • _cons | 5 .6324555 7.91 0.004 2.987244 7.012756 • ------------------------------------------------------------------------------

More Related