The requirements are the same as for Homework 3.

Include the R code in your pdf file. Also attach your R file.

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Open the file Law_schools.xls. The data is presented in 18 columns, standing for 1. rank law school ranking 2. salary median starting salary 3. cost law school cost 4. LSAT median LSAT score 5. GPA median college GPA 6. libvol no. of volumes in libraries, 1000s 7. faculty no. of faculty 8. age age of law sch., years 9. clsize size of entering class 10. north =1 if law sch in north 11. south =1 if law sch in south 12. east =1 if law sch in east 13. west =1 if law sch in west 14. studfac student-faculty ratio 15. top10 =1 if ranked in top 10 16. r11_25 =1 if ranked 11-25 17. r26_40 =1 if ranked 26-40 18. r41_60 =1 if ranked 41-60

Problem 1 The natural logarithm of the median starting salary for new law school graduates is modeled by z = ?₀+ ?₁x₁+ ?₂x₂+?₃ln x₃- ?₄x₄, where z = ln y, where y- median starting salary x₁- LSAT x₂- GPA x₃- cost x₄- rank

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Do not use Excel. Modifications if needed in R directly. (i) Perform analysis of Gauss-Markov assumptions using R. (ii) Use R to find the estimators of the parameters of the model (?_i). Clearly state the model with the found coefficients. Find the 95% confidence intervals for each parameter of the model. (iii) Use R to find the coefficient of determination and interpret it. (iv) For testing hypotheses: H₀:?_i = 0 H₁:?_i > 0, for i = 1, 2, 3, 4. find t-statistics. Then on paper show how to use them to make conclusions (do not use p-values). If for some i (i = 1, 2, 3, 4) you do not reject H₀ , remove the corresponding variables from consideration. Run regression again. State the new model. Compare the models. (v) Test the hypothesis about the correlation between independent and dependent variables (whether independent variables are jointly statistically related to the logarithm of the starting median salary within the proposed model).

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