STAT 3001 Week 3 Project Correct Answers

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Week 3 Project - STAT 3001

Date: <Enter the date on which you began working on this assignment.>

Instructions: To complete this project, you will need the following materials:

• STATDISK User Manual (found in the classroom in DocSharing)
• Access to the Internet to download the STATDISK program.

Part I. Analyze Data

Instructions

Answers

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?

1. 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

Budget

Gross

Length

Viewer

1. Would you consider this data to represent a sample or a population?

Part II. ScatterPlots

1. Create a scatterplot for the data in the Budget and Gross columns. Paste it here.

1. Explain the visual relationship between Budget costs and Gross Earnings of the movies.

1. Create a scatterplot for the data in the Budget and the Viewer Rating columns

1. Explain the visual relationship between Budget costs and Viewer Rating.

Part III. Correlation

1. Find the linear correlation between the data in the Budget and Gross columns.

1. 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

1. List the sample size and the degrees of freedom for this computation.

1. Find the linear correlation between the data in the Budget and Viewer Rating columns.

1. 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 simple-regression to determine the line-of-best fit. Use the BUDGET as your x (independent) variable and GROSS as your y (response) variable.

1. Paste your results here:

Answer the following questions related to this simple regression

1. What is the equation of the line-of-best fit?

1. 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.]

1. What is the y-intercept of the line? What does it tell you about the relationship between the BUDGET and GROSS data?

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

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

1. Find the coefficient of determination (R² 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 multiple-regression using BUDGET, GROSS, LENGTH, and VIEWER RATING. Select GROSS (Column 5) as your Dependent variable.

1. Paste your results here:

1. What is the equation of the line-of-best fit? The form of the equation is Y = b_o + b₁X₁ + b₃X₃ + b₂X₂ (fill in values for b_o, b₁, b₂, and b₃).

[Round coefficients to 2 decimal places.]

1. What would you predict for the GROSS earnings of a movie for which

• BUDGET is 35 million dollars
• LENGTH is 130 minutes
• VIEWER RATING is 7.5

1. What is the R² value for this regression? What does it tell you about the regression?

Submit your final draft to the Assignment 3 Turnitin – Week 1 area of your course. Please use the naming convention "WK1Assgn3+first initial+last name" as the Submission Title.