Ans_STA3024_Exam4A_Fall2022

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Shne STA 3024 Fall 2022 Exam 4 TEST FORM A STA 3024 Fall 2022 Exam 4 Honor Pledge: “On my honor, | have neither given nor received unauthorized aid on this examination.” SIGN your name in this box in INK Write your UFID number Questions1 -8 A fitted line plot is given below that shows the average runs scored per game versus batting average for a random sample of nineteen Major League Baseball teams in the 2022 regular season. 5.00 4.75 4.00 Average Runs per Game >~ N v Fitted Line Plot Average Runs per Game = - 0.870 + 21.31 Batting Average s 0.272046 R-Sq 45.8°% R-Sqadj) 42.6% 0.1 0.22 0.23 0.24 0.25 0.26 Batting Average 1. interpret the siope. As average runs per game increases by 1, batting average decreases by 0.870. As average runs per game increases by 21.31, batting average increases by 1. As average runs per game increases by 0.870, predicted average runs per game increases by 21.31. As batting average increases by 1, predicted average runs per game increases by 21.31. As batting average increases by 1, predicted average runs per game increases by 0.272046. X 2. The Chicago Cubs had on average 4%56 runs per game, with a batting average of 0.238. Calculate and interpret the residual. a. Residual = 4.20178. The Cubs average runs per game was 4.20178 more than predicted. b. ) Residual = -0.14578. The Cubs average runs per game was 0.14578 less than predicted. €. Residual = 0.426. The Cubs batting average was 0.426 more than predicted. d. Residual = -85.325. The Cubs average runs per game was 85.325 less than predicted. e. Residual =0.14578. The Cubs batting average was 0.14578 more than predicted. residual= y -3 4= -0-870 + 2131 (0.236) =4 056— K A0178 = ¥ 20/78 — ~ W1i = D

Sh ne STA 3024 Fall 2022 Exam 4 TEST FORM A pOSiAve r=/R%=JVousg = O0.b717 becamere 3. What is the value of the correlation coefficient? a. 0.458 b. 0.426 @o.(m Additional Minitab output is given below. Coefficients Term Coef SE Coef T-Value P-Vaiue Constant -0.87 1.36 -0.64 0.531 Batting Average 21.31 563 3.79 0.001 The assumptions for inference are met. S/q;e':s‘ Pos;f,vg d. 0.272 e. 0.870 4. Calculate the 95% confidence interval for the slope of the population regression line. a. (-3.7,2.00) b. {-0.03,42.65) b T¢E (8655 (9.43, 33.19) d. (15.68,26.94) e. (18.43,24.19) = (9.43, 33.19) =131t 3.110(5.63) A significance test is performed to see if there is significant evidence of a linear relationship between average runs per game and batting average for teams in MLB. 5. What is the hypothesis? a. Hypf+#0vs.Hy:f =0 Hy:B=0vs.H;:B+0 ¢. Hy:b<Ovs.Hy;:b=0 d. Ho:b>0vs.Hy:b#0 6. What conclusion would you make for this significance test? a. With a p-value of 0.531, there is very strong evidence of a linear relationship between average runs per game and batting average for teams in MLB. b. With a p-value of 0.001, there is no significant evidence of a linear relationship between average runs per game and batting average for teams in MLB. c. With a p-value of 0.531, there is no significant evidence of a linear relationship between average runs per game and batting average for teams in MLB. With a p-value of 0.001. there is verv strong evidence of a linear relationship between average runs per game and batting average for teams in MLB.

e STA 3024 Fall 2022 Exam 4 TEST FORM A 7. Which of the following are tru7_.’a 850 a. Asignificance test for a pgsitive Jinear relationship between average runs per game and batting average would have a p-value of 0.0005. v~ ALHOWF i /Co.f + pvalue = 000 = 0.0008 b. Testing Hy: 8 = 0 is the same as testing that there is no correlation between x and y. An ANOVA test for a linear relationship between average runs per game and batting average would have a test statistic of F = 14.36.\/fi 2= F, 3:792 = 1436 d.} All of a, b and c are true. €. None of a, b and c are true. Questions 8 — 12 Census at School is an international classroom project that gives students in grades 4 — 12 experience with problem solving in statistics. The students complete a brief online survey and the results can then be used for statistical analysis. A random sample of 74 12th grade students is taken and data is collected on arm span (cm), height (cm) and gender (male/female). Gender is coded as 1 = male and O = female. Assume no interaction. 8. The regression equation for predicting arm span using only gender is § = 158.46 61/9%, where § is the predicted arm span, and x is gender. Interpret the coefficient of gender. N ™ Goep(ienk of 19.79 cm is the difference in the predicted arm span for males and females. , . . (3 b. 13;3 cm !s ::e pre:!c:e: arm span :or ;naIeT. Mades 3\: 154 \; 2 0 c. .79 cm is the predicted arm span for females. ales Y= I1S€.4b + 1534 0) d. 158.46 cm is the difference in the predicted arm span for males and females. e. 158.46 cm is the predicted arm span for males. Minitab output is given below for the multiple regression model that predicts arm span from both height and gender explanatory variables. Gender is coded as 1 = male and 0 = female. Coefficients Analysis of Variance Term Coef SECoef T-vValue P-Value Source OF SS MS F-Value P-Value Constant 30.5 341 0.90 0.373 Regression 2 9301.7 46509 31.63 0.000 Height 0.787 0.209 3.76 0.000 Error 71 10439.2 1470 Gender 7.29 4.36 167 0.099 Total 73197409 The regression equation is § = 30.5 + 0.787x; + 7.29x,, where J is the predicted arm span, x, is height and x, is gender. 9. What is the predicted arm span for a female who is 162 c¢m tall? a. 7.29cm B _ b. 30.5cm ><| = o3 ) Xa =0 157.99 cm ~ ) A . @ 165.28 cm Y- 30.5+ O~737(/6&) F1.26 (0) e. 121148 cm - /57. qq

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Shne. STA 3024 Fall 2022 Exam 4 TEST FORM A 10. What is the regression equation for males? @ 9 = 37.79 + 0.787x, Males x=1 § = 30.5+ 0.787x AN _ o Cg Ix, + 12901 C. y—31.2+7.29x21 \‘9'30 5+ 0- 181X, () d. =305+ 7.29x- 30.5+71 in) +0.1€7x, 9: 5719 + 0.767x, 11. Interpret the coefficient of height, 0.787. For either gender as height increases by 1 cm, predicted arm span increases by 0.787 cm. b. For either gender as arm span increase by 1 cm, predicted height increases by 0.787 cm. ¢. For males, as height increases by 0.787 cm, predicted arm span increases by 1 cm. d Far femalac acarm cnan increacec hv N 787 erm heioht increacec hv 1 rm 12. Given the following two statements: | If a categorical explanatory variable has three categories, use two indicator/dummy variables in the regression model. il The regression line for predicting arm span from height for males will be parallel to the regression line for predicting arm span from height for females. Which do you agree with? a. lonly b. llonly Both tand I A Naithar Af thAam

a\ﬂQ/ STA 3024 Fall 2022 Exam 4 TEST FORM A Questions 13 - 18 Using the MLB data to predict average runs per game, another explanatory variable is added to the model. This new explanatory variable is average stolen bases per game. The model is predicting average runs per game using batting average and average stolen bases per game. Use a significance level of a = 0.05. Some statistical output is given below. Correlations Average Runs per Game Batting Average Avg Stolen Bases Average Runs per Game 10000 0.6766 Batting Average 6.6/60 1.6600 Avq Stolen Bases i i 1.0000 Coefficients Analysis of Variance Term Coef SECoef T-Value P-Value Source DF _ SS MS _ F-value P-Value Constant -0.86 1.49 -0.58 0.570 Reqresswn 2 1.06206 0.53103 6.75 0.007 Batting Average 21.30 589 361 0.002 Error 16 1.25813 007863 Total 18 2.32019 Avg Stolen Bases -0.007 0.431 -0.02 0.987 13. True or False? The correlation matrix shows that average runs per game and avg stolen bases has a stronger correlation than average runs per game and batting average. 01\/3 uns pers \game vs Vg SR (= ~0.1237 a. True False a\/j nens P@r\yaﬂ/w VS, babfiy Qv = 0.676i 14. What is the multiple regression equation? (C? average runs per game = —0.86 + 21.30(batting average) — 0.007(avg stolen bases) average runs per game = 1.49 + 5.89(batting average) + 0.431(avg stolen bases) c. average runs per Game = —0.58 + 3.61(batting average) — 0.02(avg stolen bases) average runs per Game = 21.30 + 5.89(batting average) + 3.61(avg stolen bases) Qa_ éfi_@g = 40630k _ = O‘U’Sg 15. Calculate R? for this muitiple regression model. - SS{ofa/ a.3019 a. 0.280 0.458 c. 0.542 d. 0.844 e. 2,185 16. Is there significant evidence that the overall model is adequate for predicting average runs per game? a. The Ftest statistic is 6.75, which is greater than a = 0.05. There is significant evidence that the overall model is adequate for predicting average runs per game. b. The F test statistic is 6.75, which is greater than a = 0.05. There is no significant evidence that the overall model is adequate for predicting average runs per game. @ The p-value 0.007 is less than a = 0.05. There is significant evidence that the overall model is adequate for predicting average runs per game. d. The p-value 0.007 is less than a = 0.05. There is no significant evidence that the overall model is adequate for predicting average runs per game. e. The p-value 0.570, which is greater than a = 0.05. There is no significant evidence that the overall mode! is adequate for predicting average runs per game.

Shne STA 3024 Fall 2022 Exam 4 TEST FORM A 17. Which of the explanatory variables are significant for predicting average runs per game? Batting average only /DC(,C’}‘)Cy a\<7 , /0 VvoSue = O0.0032 5. Avg stolen bases only SHp-valuwe = 0. 787 ¢. Both batting average and avg stolen bases d. Neither batting average nor avg stolen bases 18. The assumptions independent random samples and normal distribution of y at fixed values of the explanatory variables are met. A standardized residual plot for batting average is given below. Residuals Versus Batting Average {response is Average Runs per Game) Standardized Residual o2 022 023 024 025 0.26 Batting Average Are the linear and equal standard deviation assumptions met for this explanatory variable? a. Thereis a leftover “U” shaped pattern, the linear assumption is not met; the variation in y-values around the residual = 0 line is similar, the equal standard deviation assumption is met. b. There is no leftover pattern, the linear assumption is met; the variation in y-values around the residual = 0 line is low for small values of batting average and high for large values of batting average, the equal standard deviation assumption is not met. c. Thereis a leftover “U” shaped pattern, the linear assumption is not met; the variation in y-values around the residual = 0 line is low for small values of batting average and high for large values of batting average, the equal standard deviation assumption is not met. @ There is no leftover pattern, the linear assumption is met; the variation in y-values around the residual = 0 line is similar, the equal standard deviation assumption is met. Questions 19 - 21 Two of the questions asked by the General Social Study is the respondent’s annual income and whether they donate to charity. Let x = annual income (thousands of doliars) and y = donate to charity (1 = yes, 0 = no). Using data adapted from the General Social Study for a random sample of fifty Americans, the logistic regression equation to predict the probability of donating to charity using annual income is e —0.258+0.0368x P = 1 o-0258+00368x 19. Does annual income have a positive or negative effect on donating to charity? Positive b. Negative 0. 0368 /s poc,Ave j Aigher income /U.JA OSA mated /Or‘o’babu ‘/y 9[ CZO/)a,(fZ‘y %j C/'aﬂ/.fi ‘

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Shne STA 3024 Fall 2022 Exam 4 eg TEST FORM A -0 Lo IO:O( th('%>’: <OO365> 10l 20. Find the approximate annual income at which the estimated probability of giving to charity is 0.5. a. $143 b. $440 @ $7010 d. $13587 e. $50000 21. The first quartile annual income in the survey was approximately $18,000. Find the estimated probability of donating to charity for this annual income. Use x =18. a. 0.44 ~0.258 + 0.0368(I¢ @. 0.60 fp\: < il -( ) !—ﬂg— = 0.60 7 e |4 @ 0358 100368 ( /&) T d. 1.50 e. 2.50 Questions 22 - 23 You decide to invest $1000 in a savings account that pays 7% interest compounded annually. A scatterplot of the balance in your savings account over the next 50 years, normali probability plot and a residual plot are given below. Fitted Line Plat Residual Plots for Savings Normal Probability Plot Versus Fits . 10000 * M * " : - ot = 5000 * g ' 3 \.~ o o 50 - z o, ° E ¢ $ ~°~ o. o« [] \ '0. b ’ W * ' . -5000 -5000 0 5000 10000 [ 6000 12000 18000 24000 Residual Fitted Value Histogram Versus Order ® 10000 * { » > 12 = 5000 4 .0 € | 3 O, . F] | I— ° s, . s | ] 7 oy, . g | & '8, * o | [ 0 '...' o . [ . . - 1 | ] | | | W oL ! g e e 3000 0 3000 5000 9000 15 10 15 20 25 30 35 40 45 SO Residual Observation Order 22. Does a linear model seem reasonable for this data? a. Yes, the fitted line plot has a straight line drawn through the data. No, the scatterplot does not show a linear trend, the points on the normal probability plot are not in a straight line which fails the normality assumption, and the residual plot shows a left-over pattern which confirms there is not a linear trend. 23. True or False. To fit a linear model to this data and conduct inference, a log10 transformation could be carried out on either the response variable, or on both the response and explanatory variables to see which transformation seems best for the data. True b. False

Ans_STA3024_Exam4A_Fall2022

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