Question

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: ??????? = ?? + ???????????? + ???????????? + ??????????? + ?0123?

Model B: ??????? = ?? + ???????????? + ??????????? + ?012?

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.
2
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.
3
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.

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

Answer 1

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: ??????? = ?? + ???????????? + ???????????? + ??????????? + ?0123?

Regression Analysis
	R²	0.915
	Adjusted R²	0.906	n	32
	R	0.957	k	3
	Std. Error of Estimate	388380.722	Dep. Var.	Concert Revenue
Regression output						confidence interval
variables		coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	a =	294,318.169
Attendance	b1 =	59.162	3.491	16.947	2.98E-16	52.011	66.313
# of concessions	b2 =	2,506.230	29,519.840	0.085	.9329	-57,962.420	62,974.881
Billboard Charts	b3 =	-7,980.320	2,311.354	-3.453	.0018	-12,714.914	-3,245.726
ANOVA table
Source	SS	df	MS	F	p-value
Regression	45,625,013,698,720.700	3	15,208,337,899,573.600	100.82	4.09E-15
Residual	4,223,508,396,681.690	28	150,839,585,595.775
Total	49,848,522,095,402.400	31
Predicted values for: Concert Revenue
				95% Confidence Interval		95% Prediction Interval
Attendance	# of concessions	Billboard Charts	Predicted	lower	upper	lower	upper	Leverage
50,000	5	15	3,145,256.45	2,881,523.75	3,408,989.14	2,307,119.48	3,983,393.42	0.110

Model B: ??????? = ?? + ???????????? + ??????????? + ?012?

Regression Analysis
	R²	0.915
	Adjusted R²	0.909	n	32
	R	0.957	k	2
	Std. Error of Estimate	381674.877	Dep. Var.	Concert Revenue
Regression output						confidence interval
variables		coefficients	std. error	t (df=29)	p-value	95% lower	95% upper
Intercept	a =	308,223.220
Attendance	b1 =	59.181	3.424	17.284	8.23E-17	52.178	66.184
Billboard Charts	b2 =	-7,992.387	2,267.147	-3.525	.0014	-12,629.224	-3,355.550
ANOVA table
Source	SS	df	MS	F	p-value
Regression	45,623,926,448,881.800	2	22,811,963,224,440.900	156.59	2.87E-16
Residual	4,224,595,646,520.690	29	145,675,711,948.989
Total	49,848,522,095,402.400	31
Predicted values for: Concert Revenue
			95% Confidence Interval		95% Prediction Interval
Attendance	Billboard Charts	Predicted	lower	upper	lower	upper	Leverage
50,000	15	3,147,385.74	2,893,565.95	3,401,205.53	2,326,544.23	3,968,227.25	0.106

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?
(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.

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

3. [1 pt] What is an approximate 95% prediction interval for the concert listed in the previous question?
(c) [$2.368M, $3.922M]

4. [1 pt] Which of the following statement is correct?
(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.

5. [1 pt] Is it appropriate to use model A as a final model to estimate the revenue of a concert?
(c) No, because not all independent variables are statistically important. Thus, revision is necessary.

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

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?
(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.