..ooo Ultra 6:57 PM X Final Exam - Ques (7) Discuss the relationship between F a
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..ooo Ultra 6:57 PM X Final Exam - Ques (7) Discuss the relationship between F and R' and construct the ANOVA table based on R (15 points) n-3) weexplaine-var iance RSS RSS n explained variance Source of variation Sum of square (SS) MSSsSd Due to segression (ESS) Rk-I) Due to residual (RSS) (I-R2KW:1-RYQy,Wth4) Total (TSs) (8) Why we need the adjusted R? (5 points) (9) Discuss when to add additional explanatory variables (1) Given the various regression results, which model would (2) Test the overall significance of cach estimated regression to a model: (20 points) you choose and why? model. (3) If a regression model is the correct model, but you estimate other models, why? (4) How would you decide if it is worth adding other variables to the model? Which test would you use? Show the necessary calculations. -Ry-Ray-of paramctersin the-or model) Bonus Questions: (10 points) (1) What is sampling distribution and why it is necessary for hypothesis testing for regression coefficients? (2) Why is normal distribution necessary for error term and estimated regression coefficients Open With PrintExplanation / Answer
(7) If all the assumptions hold and you have the correct form for R2 then the usual F-statistic can be computed as
F= [R2 /(1R2)]×[df2/df1]
This value can then be compared to the appropriate F distribution to do an F test. This can be derived/confirmed with basic algebra.
(8) The adjusted R2 is a modified version of R2 that has been adjusted for the number of predictors in the model. The adjusted R2 increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance.
(9) When we are getting lower value of adjusted R2 and want to increase the accuracy of the model, then in that case we need to add additional explanatory variables.
(9.1) Different models can be compared using checking the values of adjusted R2 and checking whether all the variables in the model are coming out to be significant or not.
Higher adjusted R2 value is preferred over the lower one.
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