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Consistency

Consistency. Clive W. J. Granger: “If you can’t get it right as n goes to infinity, you shouldn’t be in this business.” . Consistency.

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Consistency

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  1. Consistency Clive W. J. Granger: “If you can’t get it right as n goes to infinity, you shouldn’t be in this business.” 

  2. Consistency What is consistency? If an estimator, , is consistent, then the distribution of becomes more and more tightly distributed around as the sample size grows. As the distribution of collapses to the single point .

  3. Consistency In the general model: , all OLS parameter estimators are consistent.

  4. Example Trying to estimate the mean or average human IQ: In Minitab take samples of 10, 100, and 1000. Have Minitab compute the sample mean, , and the standard error of the sample mean, . A 95% CI can be created. Data can be plotted.

  5. Testing MLR Assumption 5 MLR Assumption 5: The error, u, has the same variance given any values of the explanatory variables. This is the assumption of homoskedasticity. Run a MLR analysis and graph the residuals vs. each predictor variable and vs. fits and vs. order.

  6. Testing MLR Assumption 5 Use SMOKE data set Response: cigs Predictors: educ, cigpric, age In Minitab under Regression -> Regression click on the Graphs box and at the bottom select the three predictor variables to plot the residuals vs. these variables.

  7. Testing MLR Assumption 5 – Examples of Heteroskedasticity

  8. Testing MLR Assumption 5 – Examples of Heteroskedasticity

  9. Testing MLR Assumption 5 – Examples of Heteroskedasticity

  10. Testing MLR Assumption 6 MLR Assumption 6: The error, u, is independent of the explanatory or predictor variables and is normally distributed with mean zero and variance . Run a MLR analysis and make histogram of residuals and normal probability plot of residuals.

  11. Testing MLR Assumption 6 – Examples of Normally Distributed Residuals

  12. Testing MLR Assumption 6 – Examples of Normally Distributed Residuals

  13. Testing MLR Assumption 6 – Examples of Non-Normally Distributed Residuals

  14. Testing MLR Assumption 6 – Examples of Non-Normally Distributed Residuals

  15. Testing MLR Assumption 6 – Examples of Normally Distributed Residuals

  16. Testing MLR Assumption 6 – Examples of Normally Distributed Residuals

  17. Testing MLR Assumption 6 – Examples of Non-Normally Distributed Residuals

  18. Testing MLR Assumption 6 – Examples of Non-Normally Distributed Residuals

  19. Testing for Assumptions of Normality and Homoskedasticity Use the data set 4th Graders Feet Regress foot length on childs age Comment on normality and homoskedasticity assumptions.

  20. Testing for Assumptions of Normality and Homoskedasticity Use the data set TWOYEAR Regress lwage on jc Comment on normality and homoskedasticity assumptions.

  21. Testing for Assumptions of Normality and Homoskedasticity Use the data set SMOKE Regress cigs on age Comment on normality and homoskedasticity assumptions.

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