Attached data set and the questions for opre 3360. There are 7 questions that needs to be answered.

Attendance # of concessions Billboard Charts Concert Revenue 30650 8 56 1531762 80997 1 87 4047180 93686 8 24 5805972 44405 4 99 2516538 77767 4 39 4197208 95780 7 35 6226065 82701 7 86 4123048 50165 8 29 3465110 50619 5 93 2843474 36259 7 86 1866318 52013 5 35 2670798 97447 7 71 5756817 69982 7 97 3681670 31789 10 72 2072149 39787 6 89 1964361 63596 5 65 3150802 73159 5 41 5064323 51172 8 1 2901564 54187 9 17 3170058 56681 7 1 3316764 78466 7 86 3825369 65132 8 86 2983563 52866 4 8 3091641 39536 2 20 3068049 32541 1 53 1796727 36441 1 60 2011990 74987 6 58 4389931 33791 8 81 1545359 64961 6 94 3792136 61429 3 86 2695672 68178 4 50 4147528 85701 5 52 5335423 OPRE 3360: Managerial Methods in Decision Making Under Uncertainty Graded Group Assignment 3: Regression This group assignment is open book and notes. However, once you start the problem set, you must do your own work within your study group and not give or accept help from anybody other than your group. The problem set covers the topics we learned in Class 9-12. I expect a student who is well prepared will correctly solve about 80% to 90% of the problems. Some of these questions require judgment, and may seem to have more than one precisely correct answer. Choose the best answer among the choices given. [Concert Nation] Concert Nation, INC. is a nationwide promoter of rock concerts. The president of the company wants to develop a model to estimate the revenue of a major concert event at large venues (such as Ford Field, Madison Square Gardens) for planning marketing strategies. The company has collected revenue data of 32 recent large concert events. For each concert, they have also recorded the attendance, the number of concession stands in the venue, and the Billboard chart of the artist in the week of each event. This data is available in \"Tickets\". They have two potential models that could explain the revenue. The two competing models are: Model A: = 0 + 1 + 2 + 3 + Model B: = 0 + 1 + 2 + Run regression on both models. Use only the regression outputs of the two models and the original data to answer questions 1 to 7 below. 1. [1 pt] Let's consider the model A first. What does the result of F-test indicate? (a) The p-value of F-test is 100.83. Thus, the model does not significantly explain the revenue. (b) The p-value of F-test is close to zero. Thus, all independent variables in the regression model are statistically significant. (c) The p-value of F-test is close to zero. This indicates that at least some independent variables in the regression model significantly explain the revenue. (d) This indicates weak evidence of a linear relationship, because the p-value is very low. 1 2. [1 pt] If we use model A for prediction, what is the point estimate for the revenue of a concert that has attendance of 50,000 people, 5 concession stands, and the song ranked in no. 15 in the Billboard ranking? (a) $3.145 M (b) $2.851 M (c) $3.252 M (d) $340K 3. [1 pt] What is an approximate 95% prediction interval for the concert listed in the previous question? (a) [$2.757M, $3.533M] (b) [$2.463M, $3.239M] (c) [$2.368M, $3.922M] (d) [$2.074M, $3.628M] 4. [1 pt] Which of the following statement is correct? (a) The estimated slope for the attendance is only $59.2. This means that, when keeping everything else the same, the revenue does not depend much on the attendance. (b) The t-statistic associated with the slope for the attendance variable is 16.9. This means that there is too much noise to determine if the slope is definitely positive. (c) The p-value for the concession variable is 0.933. This means that the number of concession stands is not a statistically significant variable to determine the revenue. (d) The p-value for the concession variable is 0.933. This means that the number of concession stands is a statistically significant variable to determine the revenue. 5. [1 pt] Is it appropriate to use model A as a final model to estimate the revenue of a concert? (a) Yes. All independent variables are statistically significant. (b) Yes, because the analysis indicates a linear relationship between revenue and attendance. (c) No, because not all independent variables are statistically important. Thus, revision is necessary. (d) No, because some of the slopes were negative. Thus, revision is necessary. 2 6. [1 pt] Now, consider model B. According to model B, what is a point estimate for a concert that has attendance of 50000 people, 5 concession stands, and the song ranked in no. 15 in the Billboard ranking? (a) $3.147M (b) $2.839M (c) $7.139M (d) $13.637M 7. [1 pt] Based on the regression outputs, which model would you consider more suitable for predicting the revenue between the two models- Model A and Model B? (a) Model A is more suitable, because it has a higher 2 , lower standard error of the estimates ( ), and lower F-test p-value. (b) Model A is more suitable because the fraction of SST accounted for by the residuals is higher than for model B. (c) Model B is more suitable, because, while both models have similar 2 and F-test p-value, model B has lower standard error of the estimates ( ) and all independent variables are statistically significant. (d) Model B is more suitable, because the slope coefficient is larger in magnitude. 3