Question

In Hollywood, most nightclubs hire "promoters", or people who walk around near the nightclub and try to convince passersby to enter the club. One of the nightclub owners asked a marketing consultant to estimate the effectiveness of such promoters in terms of their ability to attract patrons to the club. The consultant did some research and found that the main entertainment at the nightclubs were on Hollywood Boulevard. He collected data from 25 similarly sized nightclubs on or near Hollywood Boulevard on Saturday 11/18/17 and hypothesized the following model: People; = B1 + B2Promo¡ + BzGogo; + Ui where People; = Attendance at the ith nightclub at midnight on Saturday 11/18/17 Promo; = number of promoters working at the ith nightclub that night Gogo; = number of dancers working at the ith nightclub that night Using the data he collected, he came up with the following estimates (standard errors in parenthesis) People; = 162.8 + 25.3Promo; + 27.9Gogo (21.7) (11.8) (7.2) R2 = 0.57 a) Interpret the regression results. Do the results make economic sense? How do you interpret the value for R2 in this case? b) Which variables are statistically significant explaining the attendance at nightclubs at the 5% level? At the 1% level? c) Test the joint hypothesis that all coefficients are equal to zero at the 5% level. d) What is the expected attendance at a nightclub with 5 promoters and 5 dancers? e) Assume that dancers earn about as much per hour as promoters. If the equation is accurate, should the nightclub owner hire one more promoter or one more dancer if they want to increase attendance? Explain your answer

Please save my life by answering all parts of this question.
Thank you so much!!

Answer 1

a) The number of promoters and dancers are affect the attendance positively. Increase in 1 promoter can increase the attendance by 25.3 units and increase in 1 dancer could raise the attendance by 27.9 units. Yes we can say that these variables make economic sense as promoters and dancers can raise the attendance.

R squared = 0.57. means these two variables area able to explain 57% variation in variable people or the attendance.

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b)

for significance test we will calculate the t value for both coefficients:

for promoters: t = 25.3/11.8 = 2.14 at 5% the critical t is: 1.717 :

as 2.14 > 1.717 thus the coefficient on promoters is significance at 5% level.

at 1% level critical t (at alpha=0.01, df = 22) = 2.508

as 2.14 < 2.508 so this coefficient is not significant at 1% level.

for dancer variable:

t = 27.9/7.2 = 3.875 .... the critical t at 5% is 1.717 as we can compare the value and see that 3.875 > 1.717 thus the coefficient on dancer variable is significant at 5% critical level.

critical t at 1% : 2.508 as we can compare and see that 3.875 > 1.717 so this coefficient is significant at 1% level also.

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c)

use F test for Joint hypothesis.

F statistic = [R_squared/(1-R_squared)][n-k-1/k] = [0.57/0.43][22/2] = 14.58

the critical F at 0.05,22,2 = 3.44

as F > 3.44 we can say that both non zero coefficient as we can reject the null hypothesis.

d)

People = 162.8 + 25.3 * 5+ 27.9*5 = 428.8

at 5 dancers and 5 promoters the expected attendance is 428.8

e)

this is simply the question to see which coefficient is bigger among those.

27.9 > 25.3.. thus the nightclub must hire one more dancer as it would increase the attendance by a large amount.