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test 3 fall old - Use the foliowing to answer question i...

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Unformatted text preview: Use the foliowing to answer question i: The height (in feet) and volume of usable lumber (in cubic feet) of 32 cherry trees are measured by a researcher. The goal is to determine if voiume of usable lumber can be estimated from the height of a tree. The results are piotted below. ' 60 -. s .f $40 ”V :2 l"‘- ’. 20 n.“ 'I'.‘I' "-- 59.0 70.0 80.0 90.0 Height ' 1. In this study, the reSponse variable is A) neither height nor volume. The measuring instrument used to measure height is the ‘ response variable. i B) height. ‘ {Claimilitnee D) height or volume. It doesn‘t matter which is considered the response. 2. The scatterpiot suggests A) neither 3) nor ‘0). y B) both a) and b) .. .. “i; QL ”there is a positive association hetween height and veltirt‘ie 5 D) there IS a curved relationship between height aria volume 3. A college newspaper interviews a psychologist about a proposed system for rating the teaching ability of facuity members. The psychologist says, “The evidence indicates that the correiation between a faculty member's research productivity and teaching rating is close to zero.” A (“correct interpretation of this statement would be (\A) good researchers are just as likely to be good teachers as they are bad teachers. Likewise ” for poor researchers. , B) good research and good teaching go hand in hand. C) good teachers tend to be poor researchers and vice versa. D) good researchers tend to be poor teachers and vice versa. Version2 i’age E income. You may correctly conciude that A) women earn less than men on the average. 13) an arithmetic mistake was made. Correlation must be positive. 2/ " C) this is incorrect because r makes no sense here. kw? “““““ D) women earn more than men on the average. 5. In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. price = «6677 + 175 x horsepower. Based on the least—squares regression line, the residual for a 1991 model car that costs $30,000 with horsepower equal to 200 would be A) «81677. B) ”85354 A .3; some + ragcme3.,:-;Z‘€i393 . \ 9w (3) $15 823 3W” R" mlwfiifl/ (a. 5L}: 0105 ~ up Fanciféireg 3 BOUQ‘D “9‘3 3’25 3:” L (g 7 ’J 6. The following scatterplot displays the 1990 per capita income versus number of deaths due to traffic accidents per 100,000 people for each of the 50 states plus the District of Columbia. 17500 ' I I I. 15000 I n I '41.! H l I ll 15 ' I . I 0 ' n 5' I .312500 -.4' ‘ ‘- ' ' I. :I' II I 10000 I 15. 0 22 5 30.0 Deaths per 100 000 People Which of the following is a plausible value for the correlation coefficient between m tea-wand MWS ‘ow lab) vet) “$ka A) +0 7 B) +0 2 C.) *1. 0 «a; D) :95 Version 2 Page 2 7. The following is a scatter-plot of the calories and sodium content of severe} brands of meat hot dogs. The least—squares regression line has been drawn in on the piot. 625 ' 10E} 12$ 150 TB Caieries Referring ‘40 the scatterplot above, based on the least-squares regression line one would predict that a hot dog containing 100 calories would have a sodium content of about B) 400. C) 600. D) 70. . A researcher wished to determine whether a company's profits can be used to predict the market vaiue ofthe Company. Based on data from a sampie of over 80 companies from the Forbes 500 iist, the researcher calculated the equation ofthe least-squares line for predicting market value from profits to be Market value x 388.2 + l3.7(Profits) The correlation between market value and profits would be ..__A) 117/3882. QQEJ/DPOSitive, but we cannot say what the exact value is. C) either FOSifiVG Or negative. It is impossible to say anything about the correlation from the information given. D) 1/13.7. 9. Which of the following statements concerning residuals is true? A) The value ofa reSidual is the observed value of the response minus the value of the response that one would predict from the feast—squares regression line. B) The sum of the residuals is always 0. ”9% A PM Of the FGSiduals is useful for assessing the fit of the ieastvsquares regression Iine. / D) ‘zAli of the above. Ks/ Version 2 Fage 3 10. When possible, the best way to establish that an observed association is the result of a cause and effect relation is by means of A) \exarnining Z~SCOICS rather than the original variables biggie wellwdesigned experiment. C) the correlation coefficient. D) the least squares regression line. Use the following to answer questions llulé: An old saying in golf is “you drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 69 money Winners on the PGA tour in 1993 are examined. The average number of putts per hole for each player is used to predict their total winnings using the simple linear regression model 1993 winningSi m fie "r flr(average number of putts per hole) 4“ a where the scatterplot is approximately linear, deviations a are assumed to be independent and normally distributed with mean 0 and standard deviation 0. This model was fit to the data using the method of least-squares. The following results were obtained from statistical software. R2= 0. 08} 37.. 281,777 Source “f Sum of Sguares Model 1 4.71605 x 10” Error 57._ 53.19690 >< l0“ Variable mm Std. Err. of Parameter Est. Constant 7,897,179 3,023,782 Avg. Putts 4,139,198 1,698,371 £1. The explanatory variable in this study rs < {9' average number of ports per hole. """ B) the slope, )8. C) -4 139 198. D) 1993 winnings. Version 2 Page 4 are A) 68. B) 281,777. __ C) 69.. Limnéli; 12. The quantity s 3 281,777 is an estimate of the error standard deviation of the simple linear regression model (also called the standard error of the residuals). The degrees of freedom for s 13. Suppose the researchers test the hypotheses H0: )3; m 0, Ha: ,Bl <0 The valuapfthe I statistic for this test is l (’1 fifl/ 5 1 / M B) 0.08 l . C) 2.6 l . D) 2.44. ,7 ~———" Ht 1 .1 . (a .__\ 14. Is there strong evidence (and if so, why) of a straight line relationship between average number of putts per hole and 1993 winnings A) It is impossible to say, because we are not given the actuaf value of the correlation. B) No, because the value of the square of the correlation is relatively smali. C) Yes, because the slope of the least‘squares fine is positive. {2)} Yes, because the analne for testing if the stope is 0 is less than 0.05. 15. Suppose we use statistical software to predict the 1993 mean winnings for all PGA tour pros who averaged 1.75 putts per hole and obtain the following output. Predicted Winnings Stdev.Predict 95.0% CJ. 95.0% P.I. 653,582 61,621 (530,559, 776,605) (77,73I, 1,229,433) A 95% interval for the mean winnings for all PGA tour pros who averaged 1.75 putts per hole is“ m... <41? A), (530,559, 776,605). 13) 653,582 d: 6r,62i. C) 653,582 a 123,242. D) (77,731, 1,229,433). 16. The correlation between 1993 winnings and average number of putts per hole is A) 0081 B) 0.285 («7/ C) -O.285 - D) 0.081 www- ”— QIQK‘ {3-, j: Q.le I: ~©,Z,%Lt—(e Version 2 Page 5 -5) W i Use the following to answer questions 17*20: A researcher was investigating possible explanations for deaths in traffic accidents. He examined data from 1991 for each of the 50 states pins the District of Columbia. The data included the number of deaths in traffic accidents (labeled as the variable Deaths), the average income per family (iabeled as the variable income), and the number of children (in multiples of 100,000) between the ages of l and 14 in the state (iabeled as the variable Chiidren). As part of his investigation he ran the following multiple regression model ' Deaths = ,80 ~i~ fl;(Children) + ,82(Income) + a where the deviations a were assumed to be independent and normally distributed with mean 0 and standard deviation 0'. This model was fit to the data using the method of ieasbsquares. The following results were obtained from statistical software. Source df Sum of Squares Mean Square F Modei 2 48362278 sum; us? get. site-s 3a EH01“ L}? 3efl~bbé3 asg'hafillS' Total 50 51404341 Variabie Parameter Standard Error of t p Estimate Parameter Est Constant 593.829 204.114 2.9093 00031 Children 90.629 3.305 27.4218 <0.0001 - income —0.039 0.015 -2.60 0.007 17. Suppose we wish to test the hypotheses Ho: )6] = fig 3 0, Hi: at ieast one ofthe @- is not 0 the F-Statistic is A) 26.209 B) below 0.0}. D) 21181139 3.4;; 3 1&8 3; 231%"; it“ 18. A 99% confidence interval for ,82, the coefficient of the variabie Income, is w,...w...~.....__...__. B) “5.015%.079. ' C) 0.015i0.104. ”‘0 so “30 it C2379? )LQ 915') Version 2 Page 6 A) 0.470. )' . 59. D) 0059. 19. The proportion of the variation in the variable Deaths that is explained by the explanatory variables Children and Income is a gamma? (2/ 3 Elites-3W .. 20. Based on the above analyses, we conclude A) the variable Children is not useful as a predictor of the variable Deaths, unless the variable Income is also present in the multiple regression model. B) the variable income is not useful as a predictor of the variable Deaths and should be omitted from the analysis. C) the variable Income is statistically significant at level 0 05 as a predictor of the variable Deaths @the variable Income is statistically significant at level 0.05 as a predictor of the variable Deaths in a multiple regression model that includes the variable Children. 21. The degrees of freedom for the SSE component of the regression analysis is A) 50 a) 49 22. Recall the Grandfather clocks example used in class. A collector of antique grandfather clocks knows that the price received for clocks increases linearly with the age of clocks. But, he wants to build a prediction model and also has data on number of bidders and a measure of condition available. Using the forward regression method, he added one variable to the model. It was significant and now he wants to choose the second variable to see if it provides additional information about predicting the price. Using the correlation matrix below, which is appropriate variable to add next? Correlation matrix: AGE NUMBIDS CONDITION RESIDUALS “T 'Humids C) Condition D) Price PRICE 072963125 039520437 079741305 060343385 AGE NUMBIDS CONDITION 412537491 0.5572251 0.4295482 " 0.4727820 0087295435 1.3158458E~16 Version 2 Page 7 .... refill.) nae. 23. An Athens statistician claims that he can predict the number of peopie that will visit a downtown restaurant on a Saturday night based on three factors: drink price (in cents), distance from the Arches (in blocks) and average iength of wait to be seated (in minutes). Convinced of this, he goes on a tour of 50 Athens bars to obtain the following output. ANOVA Df SS MS F Signi ancef Regression 13i78.7 " Residual i 46.6 Totai Coefficient Standard Error t—Stat vaaiue intercept liOO 40.275 27.31 0.000 . Price -3.3822 0.9947 3.4 " 0.027 1’ Distance 40.1500 109900 3.65 0.022 “- Wait 45.2401 8.514 —l.79 p.080 If we wished to determine the overall usefulness of the model, our F-ratio wouid be " A) err“? in” «vets-“CV“ . 0,, p 4, B) 0.022 {3: «Size (W - Ls ghee D) 0027 Use—0c . 24. Using the same computer output as in question 23 above, which of the foiiowing are significant predictors of the number of people that will visit a downtown Athens restaurant on a Saturday night at the 0.05 significance level? A) Wait B) intercept, Price, & Distance C Wait, Price & Distance ‘3‘ ' rice & Distance 25. Using the same computer output as in question 2.3 above rotating to Athens downtown refl its, does there appear to be a multicoiiinearity problem here? I B) nabie to determine C) Yes Version 2 Page 8 ...
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