Question

On a typical night in a large​ city, about​ 25,000 people attend a theatrical​ event, paying an average cost of over ​$110 per ticket. The results of a multiple regression of weekly data for the receipts in millions of​ dollars, the paid attendance in​ thousands, the number of​ shows, and the average ticket price are found below.

Write the regression model.

Receipts = −17.0253 + 0.1116 Attendance + 0.0071 ​# Shows + 0.2016 Price

1.What does the coefficient of Attendance mean in the context of this regression​ model?

1. Compared to a week with a similar number of shows and average ticket​ price, an increase in attendance is associated with an increase in receipts proportional to the coefficient of Attendance.
2. Independent of how many shows are playing or what the value of the average ticket price​ is, an increase in attendance is associated with an increase in receipts proportional to the coefficient of Attendance.
3. Since the value of the coefficient of Attendance is​ low, it does not have much impact on the receipts for a given week and is not a valuable predictor.
4. Since the value of the coefficient of Attendance is​ high, it is the main factor in determining the receipts for a given week and the other variables can be ignored.

2.In a week in which the paid attendance was​ 200,000 customers attending 30 shows at an average ticket price of $105​, what would you estimate the receipts would​ be?

About $_____________Million ​(Round to two decimal places as​ needed.)

3.Is this likely to be a good​ prediction? Why do you think​ that?

1. ​Yes, because the low R2 value indicates that the model accounts for almost all of the variation in the receipts.
2. ​No, because the low R2 value indicates that the model accounts for little of the variation in the receipts.
3. ​Yes, because the high R2 value indicates that the model accounts for almost all of the variation in the receipts.
4. ​No, because the high R2 value indicates that the model accounts for little of the variation in the receipts.

Multiple Regression Model

Dependent variable​ is: Receipts
R squared = 99.9​% R squared ​(adjusted) = 99.9​%
S = 0.0966 with 74 degrees of freedom
Source	Sum of Squares		df	Mean Square		​F-ratio
Regression	487.733		33	162.5777			17481
Residual	0.691		74	0.0093
Variable	Coeff	SE(Coeff)		​t-ratio		​P-value
Intercept	−17.0253	0.2943		−57.85			< 0.0001
Attendance	0.1116	0.0009		124.04			< 0.0001
​# Shows	0.0071	0.0046		1.55			0.1254
Price	0.2016	0.0033		61.09			< 0.0001

Answer 1

1)
option A)
Compared to a week with a similar number of shows and average ticket​ price, an increase in attendance is associated with an increase in receipts proportional to the coefficient of Attendance.

2)
Receipts = −17.0253 + 0.1116 Attendance + 0.0071 ​# Shows + 0.2016 Price
= -17.0253 + 0.1116 * 200 + 0.0071 * 30 + 0.2016 * 105
=26.6757

3)
R^2 = 0.999
option C)
​Yes, because the high R2 value indicates that the model accounts for almost all of the variation in the receipts.

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