Question

In: Statistics and Probability

Date. Recepits. paid. shows. Avg attendance. ticket pric 5/1/2007 18.6859 259.181 36 72.10 6/1/2007 20.4195 281.296...

Date. Recepits. paid. shows. Avg

attendance. ticket pric

5/1/2007 18.6859 259.181 36 72.10

6/1/2007 20.4195 281.296 36 72.59

6/1/2007 20.0656 271.121 34 74.01

6/1/2007 20.4281 272.258 33 75.03

6/1/2007 19.6621 263.937 31 73.50

7/1/2007 18.5471 252.339 29 74.50

7/1/2007 18.4206 236.118 27 78.01

7/1/2007 18.6971 235.814 27 79.29

7/1/2007 19.8380 248.756 28 79.75

8/1/2007 18.4166 228.483 25 80.60

8/1/2007 18.2825 226.567 25 80.69

8/1/2007 17.8652 224.740 25 79.49

8/1/2007 16.1950 202.309 22 80.05

9/1/2007 16.3232 200.450 21 81.43

9/1/2007 12.4829 158.183 21 78.91

9/1/2007 13.2313 174.971 23 75.62

9/1/2007 13.9584 183.636 24 76.01

10/1/2007 14.3296 187.818 24 76.20

10/1/2007 16.0449 204.293 25 78.54

10/1/2007 16.1729 210.571 27 76.80

10/1/2007 17.3821 226.011 29 76.91

11/1/2007 16.9973 236.084 34 72.00

12/1/2007 14.6261 185.169 34 78.99

12/1/2007 19.7096 254.081 34 77.57

12/1/2007 19.0420 246.524 35 77.24

1/1/2008 21.0999 258.330 34 81.68

1/1/2008 20.7393 263.764 35 78.77

1/1/2008 15.4748 215.110 31 71.94

2/1/2008 16.2711 218.639 31 74.42

2/1/2008 14.4511 200.948 31 71.91

5/1/2006 18.4072 248.614 32 74.04

6/1/2006 18.1152 243.009 30 74.55

6/1/2006 19.5138 255.470 30 76.38

6/1/2006 18.6410 249.640 29 74.67

6/1/2006 17.5541 233.734 27 75.05

7/1/2006 16.1619 213.849 26 75.10

7/1/2006 17.0159 221.610 25 76.78

7/1/2006 16.6649 215.746 24 77.24

7/1/2006 16.5649 215.374 24 77.27

8/1/2006 16.2365 209.932 24 77.34

8/1/2006 16.3029 210.385 24 77.49

8/1/2006 15.5021 199.733 23 77.61

8/1/2006 15.4114 199.256 23 77.34

9/1/2006 16.3163 209.388 23 77.92

9/1/2006 12.1098 154.716 20 78.27

9/1/2006 13.1531 171.017 20 76.91

9/1/2006 13.9269 179.533 23 77.57

10/1/2006 15.9728 198.224 25 80.58

10/1/2006 16.4737 211.902 26 77.74

10/1/2006 17.1688 224.206 27 76.58

11/1/2006 17.3730 236.193 31 73.55

11/1/2006 19.2291 259.970 32 73.97

11/1/2006 18.6967 244.124 32 76.59

12/1/2006 23.4222 269.141 33 87.03

12/1/2006 19.8776 251.616 32 79.00

12/1/2006 21.2187 271.693 32 78.10

12/1/2006 20.3516 258.335 32 78.78

1/1/2006 20.4976 245.845 30 83.38

1/1/2007 19.5098 254.128 32 76.66

1/1/2007 17.3417 231.899 28 74.78

2/1/2007 14.7775 198.277 27 74.53

2/1/2007 14.4905 194.268 27 74.59

2/1/2007 13.8928 196.232 27 70.80

2/1/2007 14.4957 199.566 28 72.64

3/1/2007 17.2296 221.171 27 77.90

3/1/2007 18.2944 249.955 29 73.19

3/1/2007 15.3800 214.013 30 71.86

3/1/2007 17.7409 247.434 31 71.70

4/1/2007 19.5766 250.425 29 78.17

4/1/2007 18.3463 233.061 30 78.72

4/1/2007 19.5848 252.013 32 77.71

4/1/2007 19.4535 256.198 33 75.93

5/1/2007 21.7175 272.738 34 79.63

5/1/2007 22.8968 299.117 38 76.55

5/1/2007 20.6534 278.326 38 74.20

5/1/2007 20.0948 266.067 37 75.52

6/1/2007 20.8585 272.599 37 76.52

6/1/2007 22.1877 283.315 36 78.87

Ticket Prices :On a typical night in New York City, about 25,000 people attend a Broadway show, paying an average price of more than $75 per ticket. Data for most weeks of 2006-2008 consider the variables Paid Attendance (thousands), # shows, Average Ticket Price ($) to predict Receipts($million).

A. Construct a 95% CI estimate of the mean receipts when attendance was 200,000 customers attending 30 shows at an average ticket price of $70.

B. Construct a 95% Prediction interval of receipts, when attendance was 200,000 customers attending 30 shows at an average ticket price of $70.

C. Explain the difference in the results in parts i) and j)

Expert Solution

Minitab output:

Regression Analysis: Recepits. paid versus shows, Avg attendance, ...

The regression equation is
Recepits. paid = - 18.3 + 0.0760 shows + 0.00703 Avg attendance
+ 0.238 ticket pric

Predictor Coef SE Coef T P
Constant -18.3199 0.3127 -58.58 0.000
shows 0.0759614 0.0006291 120.75 0.000
Avg attendance 0.007028 0.004418 1.59 0.116
ticket pric 0.238385 0.003907 61.01 0.000

S = 0.0931259 R-Sq = 99.9% R-Sq(adj) = 99.9%

Analysis of Variance

Source DF SS MS F P
Regression 3 484.79 161.60 18633.30 0.000
Residual Error 74 0.64 0.01
Total 77 485.43

Source DF Seq SS
shows 1 448.40
Avg attendance 1 4.11
ticket pric 1 32.28

Unusual Observations

Recepits.
Obs shows paid Fit SE Fit Residual St Resid
2 281 20.4195 20.6051 0.0248 -0.1856 -2.07R
5 264 19.6621 19.4683 0.0232 0.1938 2.15R
6 252 18.5471 18.8116 0.0208 -0.2645 -2.91R
23 185 14.6261 14.8148 0.0537 -0.1887 -2.48RX
54 269 23.4222 23.1030 0.0431 0.3192 3.87RX
63 196 13.8928 13.6536 0.0268 0.2392 2.68R

R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large leverage.

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 13.7702 0.0309 (13.7086, 13.8317) (13.5747, 13.9657)

Values of Predictors for New Observations

Avg ticket
New Obs shows attendance pric
1 200 30.0 70.0

A. 95% CI estimate of the mean receipts when attendance was 200,000 customers attending 30 shows at an average ticket price of $70: (13.7086, 13.8317)

B. 95% Prediction interval (PI) of receipts, when attendance was 200,000 customers attending 30 shows at an average ticket price of $70: (13.5747, 13.9657)

C. Since margin of error of PI is larger than margin of error of CI so PI is wider than CI.

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