Midterm III Spring 2008 solns

Midterm III Spring 2008 solns - 1 2 3 A recent study.r of...

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Unformatted text preview: 1) 2} 3) A recent study].r of IS shoppers showed that the correlation between the time spent in the store and the dollars Spent was 0.235. Using a significance level equal to 0.05, which ofthe following is the appropriate null hypothesis to test whether the population correlation is zero? a} Hozr=flfl b) Hflzp=0fl e] H9:;r={}.fl d) Hozpeflfl Which ofll'te following, is truc'.’ l. A study was recently conducted by Major League Baseball to determine whether there is a correlation between attendance at games and the record of home team’s opponent. In this study, the dependent variable would be the record of the home team’s opponent. ll. A correlation of -0.9 indicates a weak linear relationship between the variables. lll. A perfect correlation between two variables will always produce a correlation coefficient of+ Li}. a} I and II]. b) ll and [I]. C) III only. d) All are correct. e) None are correct. In a linear regression model. why is .13. distributed normally" a) Because 1”, is distributed normally. b) Because ofthe Central Limit Theorem. c) Because moat variables in practice are usually normally distributed. :1) Because we assume .5'r is normally distributed. e) Because [in and ii" are normally distributed, FfifiE ‘l {.‘rF 10 F: fluid. .1.st Mill: -u‘.oJ .111 mohfima Am ermd‘u; F: 6mm 0.. W's-W. = -.l.o C23 . ”4i . WW. GD tit-Elle} Mawcf‘iflto Wm. 2:) our ole-Lam‘i— uppbj hurtI amt-a to} 4) 5) 6) 7) In a ordinary least squares estimation, “least squares” refers to a) Minimizing the squared deviations of if from its mean, Y b) Minimizing the squared deviations of K from its a prediction, Yk c) Minimizing the value of R2 d) Minimizing the squared correlation coefficient, r3 e) Minimizing the squared deviations of )1 from the mean, Y Which assumption is necessary to derive fig and ,8}? a) 13(11- lX.-) = flu + [£le (linearity) b) 5, ~ N (normality) c) EL?!) 2 0 d) ELSE") = 0': (homoskedasticity) and E(E!SI) : 0 (lack of serial correlation) e) All ofthe above. In fitting a Straight line to a set of data, the computed R2 is 0.21. From this we can conclude a) The regression line slopes upward b) The error variance is not constant c) The errors are not normally distributed d) Multicollinearity is a problem 6) None of the above If R2 = 1, which of the following must also be true? 3.) Changes in X cause changes in Y b) SSE = 0 c) All of the points fall exactly on a positively sloped regression line (1) Exactly two of the are true e) All of the above are true FfiGlEZ OF 10 R‘LWJA >1- = wa- , a: " 4 55:94:14: MSIT 3000 Midten‘n III Spring 2008 A ‘ § WWmwww.A..-~..~.W-.w;‘,..."mm“... Figure 1 to the predicted value of Y? a) LetterA b) LetterB 0) Letter C d) LetterD e) LetterE to the estimated value of the error term? a) LetterA b) LetterB 0) Letter C d) LetterD e) LetterE PAGE 3 OF 10 8) In figure 1 above, which of the following corresponds 9) In figure 1 above, which of the following corresponds MSIT 3000 Midterm Ill Spring 2008 A The following applies to questions #10 through #17: A publishing company in New York is attempting to develop a model that it can use to help predict textbook sales (in 000s) for books it is considering for fixture publication. The marketing department has collected data on several variables from a random sample of 15 books: number of volumes of the book sold, number of pages per book, number of competing books on the market, advertising budget for the book, and the age of the author, SUMMARY OUTPUT ANOVA Significance df 35 MS F F Regression 4 309603270 7740.0818 13.6076 0.0005 Residual 10 5688.0730 568.8073 Total 366484000 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Intercept -1 25.3078 31.0821 -4.0315 0.0024 —1 94.5630 56.0526 Pages X1 0.1759 0.0398 4.4229 0.0013 0.0873 0.2645 Competing Books X2 -1 .5738 1.9959 -0.7885 0.4487 6.0208 2.8733 Advertising Budget in 0005 X3 1.5917 0.4445 3,5812 0.0050 0.6014 2.5820 Age of Author X4 1.6137 0.6250 2.5819 0.0273 0.2211 3.0064 10) The regression equation for this model is a) I? : —125.3078 + 0.1759Xl —1.5738X2 —-1.5917X3 +1.6137X4 b) Y : —125.3078 + 0.1759Xl —1.5738X2 —-1.5917X3 +1.6137X4 c) Y : 31.0821+ 0.0398X1+1.9959X2 + 0.4445X3 +Oi6250X4 d) Y : —125.3078 +0.1759X1715738222 +1.5917ir; +1.6137X’4 6—)er ® 5).,(f v/wW-Q— YonmLed/J W7l/Awta4iimm a) IMMWHWW Mattel; WW: MAM/f)” W’Maizo W 4) TAM—Lug W “Mu“ FREE orig- 5);. 11)If we wished to test the overall usefulness of the above model, what would be the conclusion? a) The sample size is insufficient to draw any cenclusion. b) Since the relevant p-value is 0.0005, we can conclude at a significance level of 1% that the model is useful. G) Since the relevant p-value is 0.0005, we can conclude at a significance level of 1% that the model is not useful. d) Since the relevant p—value is 0.0024, we can conclude at a significance level of 1% that the model is useful. :3) Since the relevant p-value is 0.0024, we can conclude at a significance level of 1% that the model is not useful. i2)The proportion of variation in textbook sales that is explained by using the regression model is a) 0.3448 b) 0.1552 0) 0.0735 d) 0.0005 e) Not enough information to determine. 13)How many textbooks were sampled? at) 4 b) 10 c) 14 d) 15 e) Not enough information to determine. 14) As our regression model currently stands, which of the explanatory variables are significantly related to textbook sales at a 1% level of significance? at) Only Competing Books b) Only Pages, Advertising Budget and Age of Author 6) Only Pages and Advertising Budget d) Only Competing Books and Age PAGES 0F 10 73am“mau Wild-LEW Mafia“.- PM) Loflu-DJOJLGAG- P_V°*£“"— "5/ 0.0005- Lotta“, Wait Ho‘afipss:o .«i-éf P‘vmlmLx. Sana. 0-0003 ‘ 0-0!) we. 1* cm ”sesame @ WAT 1/04).me Y M Wot ("’le R2: 56:2 _ Bo‘ibo.327e T55 3co43¥om cits 0 -‘%‘(¢/% @ 731"“ dip-.- {oi-4rf'7‘ *1 = iothdFH I‘M-1:15 @ VmaW Jug P-va/Lwa. A M) M WW F‘VWZ—D-OL TAM would 6.9. PW $62.9!le {1‘ @ .. ll 15)What is the correct interpretation of the eoefiieient on number of competing books in print? a) For every additional book in print, textbook sales drop by 15738 volumes. b) For every additional book in print, textbook sales drop by about 1,574 volumes. e) For every additional book in print, textbook sales increase by about 1,574 volumes. (1) For every additional 1.5738 books in print, textbook sales decrease by 1000 volumes. 6) For every additional thousand volumes sold, new authors decrease by 1.5738. 16) Which of the following is the point estimate for number of volumes sold if a book has 504 pages, 12 other books are on the market, the firm spent $51,000 on advertising, and the authoris 33 years old? a) 78.8893 b) 87.3045 0) 118.3856 d) 204.1968 6) 81174413 17) We would expect approximately 95% of actual observed textbook sales to be within how many thousand volumes of what is predicted by the model? a) 23.8497 b) 87.9778 (1) 175.9555 d) 47.6994 8) Not enough information to determine, 0 X; : ‘IZSTBLWE {-— b-qufswq) +— K-snsfiz) 1* x6717 {51) 1‘- Awe-2533) '- 7878g93 @ 76 beware-mix. 11m; 18)In a regression of 100 average monthly purchases on customer age, family income and family size: the estimated coefficient on customer age is —0.9705, with a corresponding 95% confidence interval of (- 2.1892, 0.2483). From this we can conclude a) As a consumer gets one year older, his or her spending increases by about O_97 dollars. b) The coefficient on age is not significantly different from 0. c) Overall, the model is useful in predicting monthly purchases. d) 95% ofthe variation in monthly purchases is explained by customer age. 6) All of the above are either false or lack sufficient information to make a determination 19)In a regression of 100 average monthly purchases on customer age, family income and family size, the estimated coefficient on family income is 0.0023. The standard error of this coefficient is 00007. From this we can conclude a) Twenty-three percent of the variation in monthly purchases can be explained by family income. 1)) Seven percent of the variation in monthly purchases can be explained by family income c) The coefficient on family income is significantly different from 0 with 95% confidence. d) The coefficient on family income is not significantly different from zero with 95% confidence. e) The p-value on family income is 3.29. [ML AW #01350 4/ mmmm > W-VW uststat =M sht- W2. = 0-0023 0.0007 0,5 04:5?” so W- valxu. 31-96 $an .541 > 031.me star aa- Mama CD = 3.23 20)Ir1 a regression of 100 average monthly purchases on customer age, family income and family size, the estimated coefficient on family size is -8.723 with a p-value of 0.2575. From this we can conclude a) Since the p-value is less than the 95% critical value 1.96, the coefficient on family size is not significantly different from 0, b) Since the absolute value of the test statistic of 33.87 is larger than the absolute value of the 95% critical value of -l.96, the coefficient on family size is significantly different from O. c) 25.75% of the variation in monthly purchases can be explained by family size. d) Since the p-value is less than 0.05, at 95% confidence, the model is not overall significant, c) Since the pevaluc is more than 0.05, at 95% confidence, the coefficient on family size is not significantly different from O. 21)The reduction in prediction error achieved by using a multiple regression model instead of the sample mean is measured by a) The standard error of the model b) The standard error ofthe slope coefficient c) The R: d) The F—statistic c) The SSE 22) Multicollinearity may cause a) The signs on the coefficients to change when a collinear variable is added to the model b) The test Statistics to be underestimated c) The p-values to be overestimated d) The standard errors of the coefficients to be overestimated e) All of the above are true Pace: 8 or 10 W its-(92w 410 ’F'VW‘: N. «(L-MW oasrs’vas‘) w. {M-‘AZ/Liéadj 23) The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon A number of different independent variables were collected. Included in these were two qualitative variables described as follows: Car Type (categorical) Whether Car has ABS Brakes (categorical) l = Four door sedan 1 = All wheel ABS ’ cars 3 = Compact thick 2 2 Rear wheel ABS 3 = no ABS 4 = Full size truck 5 = Sports car If these two variables are to be included in a regression model, how many additional variables will be needed? 24) In a multiple regression model, the adjusted R2 value a) Will always be greater than or equal to R2 b) Will always be less than or equal to R2 c) May be smaller or larger than R2, depending on the data set and variables d) Will be equal to R2 if the added variable is a dummy variable e) None of the above PAGE 9 0F '10 25)You have constructed a multiple regression model for Red’s Pizza which explains pizza slices consumed (QPlZ) by the independent variables pizza price (PPIZ), soft drink price (PSODA), income (INC) and a competition dummy variable (COMP). A new variable has LN Wm: 2; now become avallable to you: sav1ngs account balance (SAVE). Suppose the correlation Mai WM and WON-f coefficient between income and savings account 01%; g “23 W W balance is r = 0.95. Should you consider adding savings account balance to your-model? CY"— 95)- MW SAVE. JD 21) Yes; SAVE may significantly improve the #L W W predicative ability of the model since it is MW . highly reiated to the dependent variable. b) Yes; adding Variables to the model will (ED always improve its performance. a I c) No; SAVE and INC are highly correlated )Mdm‘ if km,“ "Lilo-[h 5 3 do: ‘1‘va This multicollinearity will lead to confusing b) .LO 19W “-9 4.“ W and misleading results. VW MU. l 6L“ d) NO' models With five independent variables are’not efficient. WM MAL MC 99 M {l 9.3:»:— 26) A regression ofsalary (in thousands) on age and whether an individual has an MBA degree (l = MBA, O : none) yields the following results: Coefficients Standard Error t Stat Intercept 6974447813 1808029528 0385748557 gmw M614 : i 3 Q & AGE 205471344 3903041857 5259000326 MBA 3523632164 8130027454 4334096267 W Vim/9 a rims/Lu! How is the coefficient on MBA interpreted? W MAJ-‘6 M - lbs. :5 a) A} person With a: MBA earns $6974 more 3 5, 2,34 W t an a person w1t out one. - b) A person without an MBA earns $6974 L M 5* CW - more than a person with an MBA. c) A person with an MBA earns $32236 more @ than a person without one, d) A person without an MBA earns $32236 more than a person with an MBA. e) A person with an MBA earns $2054 more than a person without one. ...
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