Econ 3060 Extra Credit Assignment Running Multiple Regression

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Los Angeles City College *

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102

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Statistics

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Jan 9, 2024

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jalayer- multiple regression output readout https://www.youtube.com/watch?v=cXiZ_t2NK1k 1. Which one is the dependent variable? Y is the dependent variable 2. Which ones are the independent variables? X1, X2, X3 are the independent variables. 3. What do we use to predict what? We use independent variables (X1, X2, X3) to predict the dependent variables (Y) 4. What needs to be all next to each other? All independent variables (X’s) needs to be all next to each other. 5. Why did we need to “check labels”? Because the descriptive labels are included in the data set 6. Where in this output are the R-square and the sample size data?’ In the regression statistics 7. Where is the p-value for the F test (overall model significance)? In ANOVA (Significant F: 0.093419957) 8. Where are the coefficients and the p-value for our t-tests and our confidence intervals for our x’s? In the last table 9. What does the R-square (0.28) tell us? Roughly 28% of the variability of Y can be explained by the entire set of independent variables that we have considered which was X1, X2, X3 10. R-square can help us show some _ predictive _______ power of our multiple regression model. 11. What does the adjusted R-square tell us? Similar to R-square except it adjusts r-square for the number of independent features used, independent variables used, and the sample size. Increase the sample size, you will get better results. Increase the number of features, you’ll pay a penalty 12. Adjusted R-square is always going to be a __ little ____ ___less_ __ than R-square

13. Adjusted R-square is one way that allows us to compare _____ between two models that we are trying to predict____ _____________ from the same ___ dependent variable with a slight different subset of variables as the dependence_ ______ 14. Higher adjusted R-square means it is a ___ better_ _______ model 15. Where is the sample size in this output? Observations (23) 16. What is the null hypothesis for the F test? H0 : B1 = B2 = B3 17. What is the alternative hypothesis for the F- test? H1: at least one of those betas above not equal to zero (Bi≠0) 18. What is H0 saying? There is no useful linear relationship between any of those three independent features and why 19. What is H1 saying? There is at least one useful linear relationship between one of them, at least one of the independent features and why. It could be all one of them, it could be one or two or couple. There are different way that it could happen 20. Why do we call it the overall test? It does a lot at once. I does not tell you the detail. 21. In this case, the P-value is greater than alpha , so we ___fail to reject _______ the null hypothesis 22. If we fail to reject H0 of the F test (in other words, if we find no evidence of overall model significance,) then we _ are not go on to do the individual t-test ______________ and ___ thow out the model and reconsider the whole situation and what you want to do about it_ __________ (7:13) 23. What are the hypotheses for the t-tests for each individual independent variable? H0 : B1 = 0 H1 : B1 ≠ 0 24. What does the H0 tell us? X1 has no significant linear relationship with y 25. What does the H1 tell us? X1 has some useful linear relationship with y (positive or negative)

26. Since p-value for x1 is greater than alpha, what do we do? Fail to reject so X1 would not be useful. X1 would not be useful linear predictor. We consider throwing it out of the model and rerun in the model. We do the same thing for x2 and x3 27. How do we write out the regression model equation? Y hat= -85 + 1.17X1 + 0.07 X2 + 0.49 X3 28. What does the 1.17 in front of x1 tell us? (think about it) The slope of X1 29. What does the -85 tell us? (think about it) Intercept 30. What does the “hat” mean? Predicted value of Y

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