Question

[Part B: Module III - Regression) [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 41 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 “Part B - Data Set for Assessment Assignment.xlsx”. They have two potential models that could explain the revenue. The two competing models are: Model A: Revenue = Bô + B^ Attendance + EA Model B: Revenue = B@ +B Billboard + € Run regression on both models. Use only the regression outputs of the two models and the original data to answer questions 14 to 20 below. 14. 12 pt) Let's consider the model A first. Which of the following statement is correct? (a) The p-value of F-test is 221.64. Thus, the model does not significantly explain the revenue. (b) The p-value of F-test is close to zero. This means that the independent variable in the regression significantly explains the revenue. (c) The regression degrees of freedom is 40 in this regression model. (d) Low p-value of F-test indicates weak evidence of a linear relationship.

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
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
31471	11	73	1989263
51172	8	1	2901864
54187	9	17	3160058
63105	11	31	3704803
57498	5	72	3209550
56380	7	43	3250222
58536	6	40	4257077
54187	9	17	3170058
56681	7	1	3316764
78466	7	86	3825369
65132	8	86	2983563

Answer 1

Model-A:

E F G H J K ? x Regression Input Input Y Range: OK $D$1:$D$42 Cancel Input X Range: $A$1:$A$421 Help Labels Confidence Level: Constant is Zero 95 8 А B D 1 Attendance #of concessions Billboard Charts Concert Revenue 2 130650 8 56 1531762 3 80997 1 87 4047180 4 93686 8 24 5805972 5 44405 4 99 2516538 6 177767 4 39 4197208 7 95780 7 35 6226065 8 182701 7 86 4123048 950165 29 3465110 10 150619 5 93 2843474 11 36259 7 86 1866318 12 52013 5 35 2670798 13 97447 7 71 5756817 14 169982 7 97 3681670 15 31789 10 72 2072149 16 173159 5 41 5064323 17 51172 8 1 2901564 18 54187 9 17 3170058 19 56681 7 1 3316764 $K$2 Output options Output Range: New Worksheet Ply: New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

Results:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.922153774
R Square	0.850367582
Adjusted R Square	0.846530854
Standard Error	443740.8766
Observations	41
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4.3642E+13	4.3642E+13	221.6387078	1.12196E-17
Residual	39	7.67933E+12	1.96906E+11
Total	40	5.13213E+13
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-6225.485937	239546.382	-0.025988645	0.979398923	-490753.7777	478302.8058
Attendance	57.12111601	3.83684168	14.88753532	1.12196E-17	49.36037118	64.88186084

14.

(a) - INCORRECT - The p-value is a probability, it cannot be 212, it will be <= 1
(b) - CORRECT - When the p-value is less than the Type-I error, the null hypothesis that β1=0 is rejected which means the independent variable's slope coefficient is significant.
(c) - INCORRECT - The regression degrees of freedom will be 1 since there is only one predictor.
(d) - INCORRECT - Low p-value indicates high evidence of a linear relationship

15.

(a) CORRECT - The slope of the attendance variable is 57.12 which means for each unit increase in attendance, the increase in revenue will be 57.12.
(b) INCORRECT - The low p-value indicates that there is enough evidence of the significant relationship
(c) INCORRECT - The intercept is negative, but this does not mean the revenue will be negative for zero attendance. This is just a consequence of the linear model fit. Note that the p-value of the intercept is also very high which means the value of the intercept is insignificant.
(d) INCORRECT - Exactly opposite; the low t-stat value indicates that the negative value is insignificant i.e. not really different from zero.

16.

Point estimate of revenue = -6225.49 + 57.12 * 35000 = 1992975

We also have the option to ignore the intercept as it is insignificant and report the value as 57.12 * 35000 = 1999200