Part I.Analyze Data

Instructions

Answers

1.Open the file Nobel Laureates & Chocolate using menu option Datasets and then Elementary Stats, 13^th Edition.This file contains information on Nobel Laureates by country and chocolate consumption. An explanation for each variable is given at the end of this file. How many observations are in this file?

2-7 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

Country

Chocolate

Nobel

Population

8. Would you consider this data to represent a sample or a population and why?

Part II. ScatterPlots

9. Create scatterplot for the data in the Chocolate (as x) and Nobel (as y) columns. Paste it here.

10. Explain the visual relationship between Chocolate and Nobel columns. Is the relationship positive or negative, based on the scatter of points around the line, is the correlation weak, moderate or strong?

11. Create scatterplot for the data in the Population (as x) and Chocolate (as y) columns. Paste it here.

12. Explain the visual relationship between Population and Chocolate. Discuss direction and magnitude of the correlation.

Part III.Correlation

13.Using Stat Disk, calculate the linear correlation between the data in the Chocolate and Nobel columns. Paste your results in the answer box.

14.Explain the mathematical relationship between Chocolate and Nobel based on the linear correlation coefficient.Be certain to include comments about the magnitude and the direction of the correlation.

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

16.Using Stat Disk, calculate the linear correlation between the data in the Population and Nobel columns.

17.Compare and contrast these two relationships:

Chocolate and Nobel Population and Nobel

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 BMI given a person's weight.Using this sample data, perform a simple-regression to determine the line-of-best fit. Use the Chocolate as your x (independent) variable and Nobel as your y (response) variable. Round to 3 places after the decimal.

18.Paste your results here:

Answer the following questions related to this simple regression

19.What is the equation of the line-of-best fit?Insert the values for b_o and b₁ from above into the equation y = bo+ b₁x. (Your equation should have an x variable)

20.What is the slope of the line?What does it tell you about the relationship between the Chocolate and Nobel data?

21.What is the y-intercept of the line?What does it tell you about the relationship between the Chocolate and Nobel data?

22.What would you predict for the number of Nobel laureates given a chocolate of 11.6 pounds? Show your calculations.

23.Let's say you know the number of Nobel laureates is 12.3 and want to find the amount of chocolate consumed. Substitute into the regression equation and find the amount of chocolate. Show your calculations.

24.Using the regression results from Statdisk, what is the coefficient of determination (R² value)?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 number of Nobel Laureates using the following 3 variables:

Nobel

Chocolate

Population

Internet

Using this sample data, perform a multiple-regression. Select Chocolate as your Dependent variable.

25.Paste your results here:

26.What is the equation of the line-of-best fit?The form of the equation is Y = b_o + b₁X₁ + b₃X₃ + b₄X₄ (fill in values for b_o, b₁, b₃, and b₄).

[Round coefficients to 3 decimal places.]

27.Use the multiple regression equation to predict the Weight of person whose

Nobel is 5.5

Population is 22

Internet is 79.5

28.Using the results from Statdisk, what is the R² value for this regression?What does it tell you about the regression?

Submit your final draft of your Word file by going to Week 3, Project, and follow the directions under Week 3 Project.Please use the naming convention "WK3Proj+last name+first initial." as the Submission Title.

Variables in Data Set

Country

Nobel laureates per million of population

Chocolate pounds consumed per person/yr

Population of country in millions

Internet