1. Open the file MOVIES using menu option Datasets and then Elementary Stats, 9^{th} Edition. This file contains some information about a collection of movies. How many observations are there in this file?

252 

2. Analyze the data in this file and complete the following table, indicating for each variable what type of data it represents.

Variable 
Qualitative/ Quantitative 
Discrete/ Continuous/ Neither 
Level of Measurement 
Rating 
qualitative 
Neither 
PGR 

Budget 
quantitative 
Discrete 
0.325200 

Gross 
quantitative 
Continuous 
20.1600,743 

Length 
quantitative 
Continuous 
93222 

Viewer 
qualitative 
Discrete 
4.39.1 

3. Would you consider this data to represent a sample or a population? 
A population because there is a measurable characteristic called parameters 
Part II. ScatterPlots
4. Create a scatterplot for the data in the Budget and Gross columns. Paste it here. 

5. Explain the visual relationship between Budget costs and Gross Earnings of the movies. 
Positive trend noted which is nonlinear. A lot of scatter noted across plot until 120 on the X axis. 
6. Create a scatterplot for the data in the Budget and the Viewer Rating columns 

7. Explain the visual relationship between Budget costs and Viewer Rating. 
Nonlinear trend noted, there is a negative association. As one varible gets larger the other gets smaller. The relationship is weak with a lot of scatter.

Part III. Correlation
8. Using Stat Disk, calculate the linear correlation between the data in the Budget and Gross columns. 
Correlation Results: Correlation coeff, r: 0.3991266 Critical r ±0.3291108 Pvalue (twotailed): 0.01589

9. Explain the mathematical relationship between Budget costs and Gross Earnings of the movies based on the linear correlation coefficient. Be certain to include comments about the magnitude and the direction of the correlation


10. List the sample size and the degrees of freedom for this computation. 
Sample size, n: 36 Degrees of freedom: 34

11. Using Stat Disk, calculate the linear correlation between the data in the Budget and Viewer Rating columns. 

12. Compare and contrast these two relationships:
BUDGET and GROSS
BUDGET and RATING
How are they similar? How are they different?
[Hint: Read Page 290 “Types of Correlation”] 

Part IV. Simple Regression
Let’s say that we wanted to be able to predict the GROSS earnings (in millions of dollars) for an upcoming movie based on the BUDGET (in millions of dollars) spent on the movie. Using this sample data, perform a simpleregression to determine the lineofbest fit. Use the BUDGET as your x (independent) variable and GROSS as your y (response) variable.
Paste your results here:

Answer the following questions related to this simple regression
14. What is the equation of the lineofbest fit? Insert the values for b_{o} and b_{1 }from above. 

15. What is the slope of the line? What does it tell you about the relationship between the BUDGET and GROSS data? Be sure to specify the proper units.
[Hint: remember that both variables are measured in millions of dollars.] 

16. What is the yintercept of the line? What does it tell you about the relationship between the BUDGET and GROSS data?


17. What would you predict for the GROSS earnings of a movie for which the BUDGET is 35? 

18. Let’s say you run out of money making the movie and you have to reduce your BUDGET by 5. What effect would you predict this would have on the GROSS earnings of the movie? 

19. Find the coefficient of determination (R^{2} value) for this data. What does this tell you about this relationship? [Hint: see definition on Page 311.] 

Part V. Multiple Regression
Let’s say that we wanted to be able to predict the GROSS earnings (in millions of dollars) for an upcoming movie based on three variables:
BUDGET (in millions of dollars) spent on the movie
LENGTH (in minutes) of the movie
VIEWER RATING
Using this sample data, perform a multipleregression using BUDGET, GROSS, LENGTH, and VIEWER RATING. Select GROSS (Column 5) as your Dependent variable.
Paste your results here:

21. What is the equation of the lineofbest fit? The form of the equation is Y = b_{o }+ b_{1}X_{1} + b_{3}X_{3 }+ b_{4}X_{4} (fill in values for b_{o}, b_{1}, b_{3}, and b_{4}). [Round coefficients to 2 decimal places.] 

22. What would you predict for the GROSS earnings of a movie for which
· BUDGET is 35 · LENGTH is 130 · VIEWER RATING is 7.5


23. What is the R^{2} value for this regression? What does it tell you about the regression? 

Subject  Mathematics 
Due By (Pacific Time)  11/02/2014 12:00 am 
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