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Unformatted text preview: University of Waterloo Stat 373
Term Test II (F10)
Date: Novemberv 3, 2010
Duration: 60 minutes
Family Name: First Name: ID. #: Si gnature: Instructor: P. Balka Instructions: fé /&/%/W o This exam has 5 pages including this cover page. The marks for each question are indicated
(total of 25). Show your work. Your grade will be inﬂuenced by how clearly you express
your ideas, and how well you organize your solutions. Stat 373 Term Test I — F10 1) Consider the CEO compensation data for 50 U.S companies discussed in class. The model variates
are Bonus paid ($1000’s), Education level (no university degree: undergraduate degree; graduate
degree), Experience (years) and company Proﬁts (millions). (Source: Business Forecasting. by J.
Hanke and D Wichern, p. 544. Pearson Prentice Hall, 2009). A linear regression model was fit to
the data to investigate the relationship between the bonus paid to CEO and the other variates. R output is provided below. Note that Edul = 1 if undergraduate degree, 0 otherwise, and Edu2 = 1 if graduate degree, 0 otherwise. Assume for the purpose of this test that all model assumptions
are valid. Model #1 Outgut Coefficients: Estimate Std. Error tvalue Pr(>t)
(Intercept) 344.8636 171.1626 2.015 0.0499 *
Exper 10.9647 4.4490 2.465 0.0176 *
Profits 0.2427 ****** **** 0.0400 *
Edul —150.8277 163.9599 —0.920 0.3625
Edu2 363.2182 163.9531 2.215 0.0318* Residual standard error: 255 on 45 degrees of freedom
Multiple R—squared: 0.4239, Adjusted Rsquared: 0.3726
Fstatistic: 8.276 on 4 and 45 DF, pvalue: 4.312e—05 a) [2] Provide the conclusion of the hypothesis test associated with the given F—statistic. Be sure to
state the conclusion in the context of y. [hwy/use z Y}/3LXIO’ << .05., , (4/6. fa ‘51:!” %/K17§27g1 3/? :0
M (mt/1U“. *Aw‘f “7L [816+ me if gx/C/lchbc/ ﬂip/7y?) ¢
ydww‘Hwq /ev¢/ z.) /e/»%¢l 1‘? C50 40AM.) b) [2] Interpret the value of the Exper parameter estimate in the context of the study.
A ﬁle/W : /0‘75‘/7 {Va/7 (ML/at year 07; Q/é/leuc 1'3 aware/(64 Va%/\ &A qua/(ye '//\L/€"J€ #‘f‘2727U /’) 6M“); 07L%¢/ Quota«Alf? fd/ €14;47%/0"\ /<I/c/ Y CWVI/V
//af427”, Stat 373 Term Test I  F10 c) [2] Interpret the value of the Edu] parameter estimate in the context of the study. [gotta ‘ /5’C)..8;L77 . —.
Affe/ “(COM‘lL/ 7C0/ {’45 cJL‘F'uJL 0F CVéJ/GALZ )l/r/57L17L M (gonub C1“: ’3 VL‘lLAM corv{¢./ I'MMIN?) ”[3166 an” Mnéce/
W“ ﬁveI‘ve a7L//’J'O.d’3 /¢.JJ fzm C603 wTI'4 M emit/6197 A e; I: C
d) [3] Provide a range of values of the test statistic, 1, associated with the null hypothesis Hr) : ﬂprtg/Hx : 0 )wvat/ue = FZ/‘fy'r/P' L‘cn‘ 1/7101;sz 3 .0171
JL/gyyc éﬂlLAL/(A: [9({W > (2.0/9!) ‘— 0 3‘5
f the? SUI/DJ 7* 0/ (011 217/7 46 7t Mama; < 1.71/1 e.) W e) [3] Recall from STAT 230, that the sample variance, $2, of a set of values { .x, ,A‘2,....X" } is H 7
Zhu at)“
: [:1 n—l 7 S With this is mind, what is the sample variance of the bonus values for this data set? 51 : ﬁg; ’11? ; J'J Off/1Q
2’7  f
“ , ’— V?
. £06»)
2 3 / _ 55. —Cf6/5.) :2 If C+0"LA./ :, f"!
K J: C'f’ﬂf’a’) ) ) I ”Z 7‘ AD. .5506)? ‘ 0’ 10’ = JZJ’S'QS’s': 02952601; 55(1‘07‘41): 25.26/15 _: f07 6.37
(PM?) 9/9 ’ l
51: {0.731151 ; /03&r7a7 Y9 Stat 373 Term TestI  F10 2) To address questions regarding the effect of education level on bonus, Y, (after accounting for
company profits and CEO experience), a second model was fit to the data: Model #2: Y = ,30 + ﬂlExper + ﬂzProfits + [13Edu + R where Edu = 1 if university degree (undergraduate or graduate), 0 if no university degree.
Output is provided below: Model #2 Output Coefficients:
Estimate Std. Error tvalue Pr(>t)
(Intercept) 288.1612 180.7063 1.595 0.11764 Exper 13.8295 4.5931 3.011 0.00422 **
Profits 0.2736 0.1215 2.253 0.02909 *
Edu —257.0601 169.2082 1.519 0.13556 Residual standard error: 271.4 on 46 degrees of freedom
Multiple Rsquared: 0.3332, Adjusted R—squared: 0.2897
F—statistic: 7.662 on 3 and 46 DF, pvalue: 0.0002955 Use the output from one or both models to perform separate hypothesis tests that address the
following questions (as with all hypothesis tests, be sure to include the null hypothesis, value and
degrees of freedom of test statistic, p—Value, and conclusion in the context of the study): i) [3] After accounting for CEO experience and company profits, is there any difference in bonus
between CEO’s who have a university degree (either undergraduate or graduate) and those
who do not? H. 3 pm c0
H“: /L’Ctr ﬁo fer} J;‘1LI’1L/Eai
f a 4527 (951367 I’VA/Kc 3 013515’6 /0 M% fédée'f Ho. ﬂare (‘3 E Jj/pjff/(wf a/z/fcng/tu
/r\ 5511“) 5c¢weon Cé’ﬂ/J w/w A4,." a mil/club aé‘ffec M /¢ua an {d 21.9% Stat 373 Term Testl — F10 ii) [6] After accounting for CEO experience and company profits. is there any difference in bonus
between CEO’S who have a undergraduate degree and those who have a graduate degree?
(Hint: the extra sum of squares procedure is required to answer this question) ’46 5 /§ 49041 ‘5 ﬂame Hai ﬂat”; 31 ﬂex“; F” W “”5”?
556/0735w/yy 3611/1 jéaea),w( = owls/"V6 : 3388226616
550695;“! ; (Zn/1W : swans/a; :9 MW 37/
/ a$§l ”Fla/77M Pat/a: fw/m xoz ﬂaw/Macaw) ~ (tjajt [40. 4f~lzr Mammal/j 79/ €50 ’i‘r/é/zﬂntt Yl CW/uy/zﬂ'hl’x CEO [J W40 Amt/c M M¢ljfwoluft [cf/cc (ﬂu/c 6 J3”); Mij
w! éonMJ f/xw *AOJC :44sz aj/ﬁOZM/JZO de/rgc. 3) [4] Use Model #1 to provide a 95% prediction interval for the bonus of a CEO with an undergraduate degree and with 30 years experience, and whose company made 200 million dollars
profit. You may use the fact that the standard error of this predicted value is 273 ($1000’s). 7(2 offal/0%lm Z’kfa/V‘L/ #0) Kick/ 3
Q 1* %'5€()3MW7 1‘ 2w = W + 130) +/5;ézoo) +25)
‘ 3W. 806 + magi/7630+ Oats/270007 . 4'03277
= 5'7/.f°‘¢ 5&‘(QMW7 : 273 f x = 6743.03: : Qﬂ/S/ 7J/Z /f fa} yhéw .'
57/471 '5 10/7/5173) 2 57/316 J’s/9.81 = (2/70) #237) /_______.,. ...
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