Universal Studios is developing a model to predict first week number of tickets sold to its non-animated movies. Universal collects information on 17 recent releases and wants to identify those characteristics that are related to TICKETS.

TICKETS

Number of tickets sold in the first week (in millions of tickets)

COST

Production plus marketing cost (in millions of dollars)

THEATRE

Number of theatres (in hundreds of theatres)

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HOLIDAY

= 1 if the movie opened on a holiday weekend

DRAMA

= 1 if the movie is a dramatic movie (ex. Twilight Saga)

ACTION

= 1 if the movie is an action adventure movie (ex. Pirates of the Caribbean

SUPERHERO

= 1 if the movie is a superhero movie (ex. Spiderman)

CMO

=1 if the movie is a comedy/musical other movie (excluded category)

The data was used to fit the following three models in which the dependent variable is TICKETS

MODEL 1:

Multiple Regression for tickets Multiple

Adjusted

R-Square

0.7922

Mean of Squares

678.7886 10.9513

StErr of

Estimate

3.3093

F---Ratio

Summary

ANOVA Table

Explained Unexplained

Regression Table

Constant cost

R

0.8973

Degrees of Freedom

1 15

Coefficient t---Value

3.9855 1.8490 0.0944 7.8729

R-Square

0.8051

Sum of Squares

678.7886 164.2702

p---Value

0.0843 0.0000

Standard Error

2.1556 0.0120

p---Value

Confidence Interval 95% Lower Upper

8.5800 0.6089 0.0689 0.1200

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MODEL 2:

Multiple Regression for tickets

Summary

ANOVA Table

Explained Unexplained

Regression Table

Constant cost theatre holiday

MODEL 3:

Multiple Regression for tickets

Summary

ANOVA Table

Explained Unexplained

Multiple

R

0.9405

Degrees of Freedom

3 13

Coefficient

Adjusted

StErr of Estimate

2.7362

F---Ratio

p---Value

0.3225 0.0180

0.0552 0.1416

R---Square

R

-

--Square

0.8846 0.8579

Sum of Mean of Squares Squares

745.7338 248.5779 97.3251 7.4865

Standard t---Value Error

p---Value

Confidence Interval 95% Lower Upper

6.6369 2.3561 0.0099 0.0883

value suppressed

1.2602 7.8848

2.1404 2.0814 1.0284 0.0491 0.0181 2.7071

1.6813 0.7985 2.1056 3.3123 2.1165 1.5650

Multiple

R

0.9569

Degrees of Freedom

6 10

R-Square Adjusted

Square -

0.9157 0.8652

Sum of Mean of Squares Squares

StErr of

Estimate

2.6654

F---Ratio

R

p---Value

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772.0149 128.6691 71.0439 7.1044

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Coefficient

Constant

cost

theatre 1.7970 holiday 4.1837

t---Value

1.8216

value suppressed 0.0066

Regression Table

Lower

Upper

1.1124 0.0961 3.6371 8.9974

6.0522 6.8679 8.0479

Standard Error

2.7367 0.0201 0.8259 2.1604 2.3351

2.0283 1.9935

Confidence Interval 95%

p---Value

drama action superhero

0.8494 2.3487 3.6062

2.1758 0.0546 1.9365 0.0816 0.3637 0.7236

1.1580 0.2738 1.8090 0.1006

0.0432 0.6301 4.3535 2.1705 0.8355

4.9852 0.0513

0.0985

11.0829

a) What is the value of the simple correlation between TICKETS and COST?

b). If you are able to determine the answer, is showing the film in more theatres associated with higher ticket sales (with cost and holiday opening held constant) with = 0.05? (Justify your response).

c) If you are able to determine the answer, do higher cost movies have higher ticket sales (with THEATRE, HOLIDAY and movie genre held constant) with = 0.05? (Justify your response).

1. d)If you are able to determine the answer, do movies opening on holiday
2. weekends have different ticket sales than those opening on non-holiday weekends (with COST held constant) with = 0.05? (Justify your response).
3. e)Interpret the coefficient for COST in Model 1 (that is, interpret the estimated value of 0.0944 without considering whether or not this value is
4. "statistically significant").
5. f)Interpret the coefficient for ACTION in Model 3 (that is, interpret the
6. estimated value of 2.3487 without considering whether or not this value is
7. "statistically significant").
8. g)Interpret the coefficient for THEATRE in Model 2 (that is, interpret the
9. estimated value of 1.6813 without considering whether or not this value is
10. "statistically significant").
11. h)Which model would you recommend to predict TICKETS with = 0.05? (Justify your response).
12. i)Based on model 3, predict TICKETS for a superhero movie opening in 3500 theatres on a holiday weekend that cost $150,000,000. Use all variables in Model 3 to obtain your prediction even if some of them are not "statistically significant".
13. j)What is the 95% prediction interval for your prediction in part i)