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 attendance at the night club will increase by 25.3 by increasing the number of promoters by 1 keeping the number of dancers constant.

The attendance at the night club will increase by 27.9 by increasing the number of dancers by 1 keeping the number of promoters constant.

With no promoters and dancers at the nightclub, we estimate the attendance at the night club to be 162.8

The slopes coefficients for promoters and dancers are positive which suggests that the attendance will increase with increase in number of promoters and dancers. Thus, the results makes sense.

Interpretation of R² - 57 % of variation in attendance is explained by the model with number of promoters and dancers as predictor variables.

b)

Degree of freedom = n - k - 1 where k is number of predictors

= 25 - 2 - 1 = 22

Critical value of t at 5% significance level and df = 22 is 2.07

Critical value of t at 1% significance level and df = 22 is 2.82

Test statistic for Promoters, t = Coeff / Std Error = 25.3 / 11.8 = 2.14

Since, the test statistic is greater than 2.07 but less than 2,82, we conclude that the number of promoters variable is significant at 5% significance level but not at 1% significance level.

Test statistic for Dancers, t = Coeff / Std Error = 27.9 / 7.2 = 3.875

Since, the test statistic is greater than 2.07 and 2,82, we conclude that the number of promoters variable is significant at both 5% significance level and 1% significance level.

c)

HO: B1 = B2 = 0

H1: At least one of the coefficients is not zero.

Test statistic, F = [R² / k] / [(1 - R²) / (n-k-1)]

= [0.57 / 2] / [(1 - 0.57)/(25 - 2 - 1)]

= 14.58

Degree of freedom = k, n-k-1 = 2, 22

Critical value of F at df = 2, 22 and 5% significance level is 3.44

Since the observed F (14.58) is greater than the critical value, we reject the null hypothesis H0 and conclude that there is strong evidence that at least one of the coefficients is not zero.

d)

The estimated regression equation is,

People = 162.8 + 25.3 Promo + 27.9 Gogo

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

The expected attendance with 5 promoters and 5 dancers is 428.8

e)

Since the slope coefficient of dancers is greater than that for promoters, we expect more attendance to increase with a unit change in number of dancers instead of promoters.Thus, the nightclub owner hire one more dancer to increase attendance.