1 / 16

Regression III

Regression III. The regression model has both constants ( , b) and variables (X, Y) The “fit” of the regression equation to the data is numerically expressed by the r 2 statistic. The b for each indep var can be tested for statistical significance using a t test.

jbuttram
Télécharger la présentation

Regression III

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. Regression III

  2. The regression model has both constants (, b) and variables (X, Y) • The “fit” of the regression equation to the data is numerically expressed by the r2 statistic. • The b for each indep var can be tested for statistical significance using a t test. • The overall model is tested for statistical significance using the F ratio.

  3. Assumptions of the regression model • Like all statistics, the regression model has a number of underlying assumptions. • T-test assumes a t distribution • z scores assumes data is normally distributed • We will discuss some of the more common ones.

  4. Multicollinearity • When 2 or more independent variables in the model are highly correlated with one another. • Result: bias in the partial regression coefficients • Test: by correlating each variable with the others • Fix: drop all but one of highly correlated variables or combine into a single variable

  5. “Dummy” variables • Regression analysis assumes the use of continuous, interval level data • Two types • dichotomous variables (two possible states) • polychotomous variables • may be nominal or ordinal

  6. Dummy variables • Dichotomous variable • male/female; Republican/Democrat • yes/no • Essentially, a case has or does not have a particular characteristic • Example: last week’s regression model predicting entry GS grade • field of education • veterans’ preference • minority female

  7. Polychotomous variables - a number of possible states • often, sometimes, rarely, never • region of country (South, Midwest, East, West) • When using exclude one of the categories • Include three 0/1 variables; eliminate one category • the excluded variable becomes the reference category

  8. Autocorrelation • A nonrandom relationship among a variable’s values at different time periods • consistent patterns such as seasonal data • Often found in time series data

  9. Autocorrelation • Result: biased t-ratios, confidence limits, and hypotheses tests • Test: plot the residuals - look for distinctive patterns • Fix: introduce another independent variable that explains some of the unexplained variance • more commonly: use a statistical model other than OLS

  10. Nonlinear relationships • OLS assumes a linear relationship (remember the straight line we drew based on the regression equation?) • Some of out data does not provide a linear relationship • economic data • population data • data with built-in growth factor

  11. Nonlinear relationships • We test for this using a scatterplot. • Does the relationship appear linear? • Fix: transform one of the variables

  12. Nonlinear relationship

  13. Nonlinear relationship

  14. Heteroskedasticity • When the effect of X on Y is not equal across all ranges of Y • Result: affects size of standard error, thus biasing hypothesis test results.

  15. Outliers • Extreme values • when a particular (or number of them) don’t seem to fit in with the other data. • Problem: can bias the regression parameters

  16. Outliers (Hong Kong and Singapore)

More Related