Question

In 2018, 14.77 million people attended a Broadway show, paying an average of more than $120 per ticket. So what variables are related to the success of a particular Broadway season? Data from the Broadway League, Inc. (www.broadwayleague.com/research/statistics-broadway-nyc/) are used to estimate the following multiple linear regression model:

Grossi=β0+β1Attendancei+β2PlayingWeeksi+β3NewProductionsi+εi

for i=1,⋯,35 . The following data are gathered for each season from 1984 to 2018:

• Gross: Gross earnings ($Millions)[JP1]
• Attendance: measured in millions[JP2]
• PlayingWeeks: Total weeks during each show performed summed over all shows; the best measure of Broadway’s overall activity
• NewProductions: The number of new productions during

Excel was used to estimate this model and the output is provided below.

Regression Statistics
Multiple R		0.922185639
R Square		0.850426354
Adjusted R Square		0.835951485
Standard Error		183.1940204
Observations		35
ANOVA
	df		SS		MS	F	Significance F
Regression	3		5915152.02		1971717	58.75192	6.84E-13
Residual	31		1040361.523		33560.05
Total	34		6955513.543

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1345.794142	340.4476833	-3.95301	0.000416	-2040.14	-651.447
Attendance	258.0733774	66.98749021	3.852561	0.000549	121.4515	394.6953
Playing weeks	-0.831807119	0.639068006	-1.30159	0.202645	-2.13519	0.471581
New Productions	12.64582072	7.912639627	1.59818	0.120147	-3.49211	28.78376

[JP1]Beginning with the 2009-10 season, "Gross" represents gross gross—which is the gross earnings before deductions. For prior seasons, “Gross” represents net gross earnings, which is the income after accounting for deductions incurred by the show.

[JP2]Note: before 2009 this is paid attendance, beginning in 2009 it is attendance

1. Interpret the estimated coefficient for PlayingWeeks. Does this make sense?

2. At the 5% level of significance, test the significance of the variable PlayingWeeks. What do you conclude?

Answer 1

from above output;

estimated coefficient for Playing weeks= -0.831807119

We may interpret the slope −0.831807119 as there is decrease in Gross earnings due to PlayingWeeks.

Now to test significance of slope of playing weeks

H0: β1 = 0    v/s     H1: β1 ≠0

P-value= 0.202645

α=0.05

p-value > 0.05

hence we accept null hypothesis at 5% level of significance.

conclusion: Failing to reject H 0 , implies that there is no linear relationship between Gross earnings and PlayingWeeks