1 / 16

Lecture 4

732G21/732G28/732A35. Lecture 4. Variance-covariance matrix for the regression coefficients. Variance-covariance matrix of the model errors/residuals. and. where. Multiple regression model (theoretical). Multiple regression model (for a sample ). ANOVA table for multiple regression.

sydney-greer
Download Presentation

Lecture 4

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. 732G21/732G28/732A35 Lecture 4

  2. Variance-covariance matrix for the regression coefficients

  3. Variance-covariance matrix of the model errors/residuals and where

  4. Multiple regression model (theoretical) Multiple regression model (for a sample)

  5. ANOVA table for multiple regression where J is a n * n matrix of ones

  6. Example data set (car prices) We have collected information about cars of a certain model. n = 59

  7. Scatter chart price/year

  8. Scatter chart price/No. kilometers

  9. Regression output from car example Regression Analysis: Price versus Year, Kilometers The regression equation is Price = - 35397446 + 17928 Year - 2.61 Kilometers Predictor Coef SE Coef T P Constant -35397446 5767248 -6.14 0.000 Year 17928 2881 6.22 0.000 Kilometers -2.6149 0.2039 -12.83 0.000 S = 30028.2 R-Sq = 90.2% R-Sq(adj) = 89.9% Analysis of Variance Source DF SS MS F P Regression 2 4.65369E+11 2.32684E+11 258.05 0.000 Residual Error 56 50494815376 901693132 Total 58 5.15864E+11

  10. Interval estimation for multiple regression Confidence interval: where Prediction interval: where

  11. Regression Analysis: Price versus Year, Kilometers The regression equation is Price = - 35397446 + 17928 Year - 2.61 Kilometers Predictor Coef SE Coef T P Constant -35397446 5767248 -6.14 0.000 Year 17928 2881 6.22 0.000 Kilometers -2.6149 0.2039 -12.83 0.000 S = 30028.2 R-Sq = 90.2% R-Sq(adj) = 89.9% Analysis of Variance Source DF SS MS F P Regression 2 4.65369E+11 2.32684E+11 258.05 0.000 Residual Error 56 50494815376 901693132 Total 58 5.15864E+11 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 415141 7201 (400716, 429567) (353282, 477001) Values of Predictors for New Observations New Obs Year Kilometers 1 2002 30000

  12. Four-in-one plot of residuals for car example

  13. Residuals plotted against predictors

  14. Example data set (car prices)

  15. Scatter chart of price/equipment level

  16. Regression Analysis: Price versus Year, Kilometers, Equipment The regression equation is Price = - 20833056 + 10618 Year - 2.08 Kilometers + 57904 Equipment Predictor Coef SE Coef T P Constant -20833056 6309217 -3.30 0.002 Year 10618 3154 3.37 0.001 Kilometers -2.0768 0.2022 -10.27 0.000 Equipment 57904 10408 5.56 0.000 S = 29269.6 R-Sq = 90.0% R-Sq(adj) = 89.4% Analysis of Variance Source DF SS MS F P Regression 3 4.22692E+11 1.40897E+11 164.46 0.000 Residual Error 55 47118909984 856707454 Total 58 4.69810E+11 Source DF Seq SS Year 1 2.82889E+11 Kilometers 1 1.13288E+11 Equipment 1 26514947048

More Related