Sample Final 2 8AM

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New York University *

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1

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Statistics

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Feb 20, 2024

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pdf

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8

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1. (31 points) Consider the following Regression Output and answer the questions that follow the output: Regression Analysis: lnsalary versus RBI Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 1 ______ _______ ______ _____ Error 335 ______ _______ Total 336 465.11 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.893174 _____% 42.37% 41.90% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 5.3926 0.0874 61.72 0.000 RBI 0.02596 0.00165 15.75 0.000 1.00 Regression Equation lnsalary = 5.3926 + 0.02596 RBI - 336 t.jjj-0.su Fstat ! st ! c n -1<-1 µ MI = 26 MSE ✓ Pvaıue SSR 20L MSR 264 412.5 T SE 264 ms-t-o.ba § > msg 㱺 ! nue 'de ⊥ se2=o SSE = ü÷ :O -79 • / ER " 2 %Ç
A. What is the value of the sample correlation between lnsalary and RBI? (4 points) B. Fill in the blanks. (12 points) C. Is there evidence that RBI is an important variable for forecasting lnsalary? Explain. (8 points) D. Construct a 90% Confidence Interval for Beta1 and provide an interpretation. (7 points) - -00 rvu = Iz s ! s ! n ⊥ ± 42 > 6- 52 × +1=6.52 ✓ compa 0 f. ✗ ! mportant for fo
2. (33 points) Consider the following regression output and the graph on the following page. The response variable is PageCost and the three continuous predictors are Circ (Circulation), PercMale(Percent of readership that is Male), and MedIncome (Median Income of Readership). Answer the questions that follow the output. Regression Analysis: PageCost versus Circ, PercMale, MedIncome Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 17219203510 5739734503 33.30 0.000 Error 44 7584600772 172377290 Total 47 24803804282 Model Summary S R-sq R-sq(adj) R-sq(pred) 13129.3 69.42% 67.34% 60.00% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -8643 12291 -0.70 0.486 Circ 5.281 0.530 9.96 0.000 1.08 PercMale -11.0 77.2 -0.14 0.887 1.38 MedIncome 1.223 0.535 2.28 0.027 1.43 Fits and Diagnostics for Unusual Observations Obs PageCost Fit Resid Std Resid 25 95575 67265 28310 2.25 R 35 97700 112068 -14368 -1.37 X 43 85870 46879 38991 3.02 R 45 77400 107486 -30086 -2.82 R X R Large residual X Unusual X < 5 ! k ! s ! arasındak ! ! l !ş k !
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A) Is there evidence that the regression model is useful? Use alpha = .05 and explain. (7 points) B) Is there evidence of (severe) multicollinearity in the model? Explain. (5 points) deoes 2 ona → appear ✓ ! . Not normal ( eps ! lon ) - - F test - VIF
C) Based upon the graphs and the output, do any of the regression assumptions appear to be violated? Are there any other issues apparent? (7 points) D) Within the context of this model, is there evidence at alpha = .02 that as MedIncome increases, PageCost decreases? (7 points) E) Would you want to use this model? Explain your answer. (7 points) - = - negat ! ve / raaı ! an # 0 ← - - B Stat ! st ! cs → -
3. (27 points) Your friend suggests that the following regression is better for the same data but with some transformations. Specifically, the response variable is now the natural log of Pagecost and ln(circ) is used in place of circ. Answer the questions that follow the output. Regression Analysis: lnPageCost versus lncirc, PercMale, MedIncome Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 15.4812 5.1604 86.54 0.000 Error 44 2.6237 0.0596 Total 47 18.1049 Model Summary S R-sq R-sq(adj) R-sq(pred) 0.244191 85.51% 84.52% 82.82% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 4.026 0.430 9.36 0.000 lncirc 0.6484 0.0404 16.04 0.000 1.15 PercMale 0.00128 0.00144 0.89 0.379 1.39 MedIncome 0.000056 0.000010 5.54 0.000 1.46 Regression Equation lnPageCost = 4.026 + 0.6484 lncirc + 0.00128 PercMale + 0.000056 MedIncome Fits and Diagnostics for Unusual Observations Obs lnPageCost Fit Resid Std Resid 24 10.1849 10.6678 -0.4829 -2.04 R 29 10.5176 10.0200 0.4976 2.09 R 30 10.9407 10.4509 0.4898 2.03 R 32 8.8846 9.3528 -0.4682 -2.03 R R Large residual A) Is there evidence that the model is useful? (7 points) Ret f- model ✓ ! s Usetull F test →
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B) Another friend states that this model is far superior to the previous one because the Rsquared value for this model is 85.51% while for the previous model it was only 69.42%. Do you agree with this statement? Be Careful and explain. (6 points) C) Is PercMale an important variable for describing ln(Pagecost)? Explain. (7 points) D) Based upon the output, what proportion of the variability in MedIncome is explained by lncirc and PercMale? (7 points) # ! . E- P value ! s loıw
4. (9 points) Consider the best subsets output for the transformed data used in problem 3. Answer the questions that follow the output. Best Subsets Regression: lnPageCost versus lncirc, PercMale, MedIncome Response is lnPageCost M P e e d l r I n c n c M c i a o R-Sq R-Sq Mallows r l m Vars R-Sq (adj) (pred) Cp S c e e 1 70.2 69.5 67.6 46.5 0.34252 X 2 85.2 84.6 83.0 2.8 0.24362 X X 3 85.5 84.5 82.8 4.0 0.24419 X X X A) Using a nested F-test, compare the model with 1 variable to the model with all three variables. (9 points) - a-

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