Stats II 4

18 flashcards · Other · by Daniel F.

1. Model assumptions for multivariate regression

   Linearity Normality Homoscedasticity Multicolinearity

2. Linearity

   Dependent variable is a linear function of the independent variables

3. Normality

   The residuals follow a normal distribution

4. Multicollinearity

   The independent variables are not perfectly correlated correlated independent variables have redundant information no new information unstable coefficients (large standard error low t-values) coefficient signs might not match expectations warning signs when variable is added large change in previous coefficients previously significant variable becomes insignificant std dev increases

5. variance inflation factor (VIF)

   how much the variance (the square of the estimate's standard deviation) of an estimated regression coefficient is increased because of collinearity usual threshold is 10

6. Dummy variables

   Qualitative variables should be recoded into a set of dummy variables. Every categoryl be compared to a reference category: m categories should be recoded into m-1 dummy variables

7. dummy trap

   m categories are coded in m dummy variables no base category

8. Nonlinear terms

   Take the natural logarithm of the original independent variable if that is more Logarithmic expressions are always interpreted in terms of percentages

9. stages of model building

   Model Specification Coefficient Estimation Model Verification Interpretation Inference

10. Model Specification

    Understand the problem to be studied Select dependent and independent variables Identify model form (linear, quadratic...) Determine required data for the study

11. Coefficient Estimation

    Estimate the regression coefficients using the available data Form confidence intervals for the regression coefficients If estimating individual slope coefficients, examine model for multicollinearity and specification bias

12. Model Verification

    Logically evaluate regression results in light of the model (i.e., are coefficient signs correct?) Are any coefficients biased or illogical? Evaluate regression assumptions (i.e., are residuals random and independent?) If any problems are suspected, return to model specification and adjust the model

13. Interpretation and Inference

    Interpret the regression results in the setting and units of your study Form confidence intervals or test hypotheses about regression coefficients Use the model for forecasting or prediction (if that is the goal)

14. Model specification

    Simultaneous method (Enter) We force all the independent variables to appear together in the model Sequential search method (Stepwise: Forward/Backward) We include independent variables in the model according to some order By correlation with dependent variable In order of significance Hierarchical method Independent variables enter in stages

15. Points to consider when including/deleting regressors

    watch out for multicolinearity use a sequential model building process compare only normalized R2 values between similar models with different number of variables

16. adjusted R2

    corrects for the fact that adding non-relevant independent variables will still reduce the error sum of squares. better comparison between multiple regression models with different number of independent variables. Penalizes excessive use of unimportant independent variables. Cannot be interpreted as % of explained variance.

17. test for autocorrelation

    Durbin-Watson d-test H0: ρ ≤ 0 H1: ρ > 0

18. Homoscedasticity

    Homogeneity of variance doesnt work well with least squares confidence intervals are invalid Hypothesis test: test on the variance of the error terms H0: Var(εi) = 0 H1: Var(εi) > 0 χ2 = nR^2