Answer all of the questions included in Parts 1 and 2 below. Be sure to answer questions using complete sentences and show all work in your calculations.
Provide a written conclusion, when appropriate, for the problem that you are addressing.
Be sure to include a paragraph or two in the last part of your paper that explains the information that you learned in the assignment. Support your paper with at least two references.
Part 1
1. Explain what a scatterplot can indicate to an investigator. What is the difference between strong positive correlation and strong negative correlation?
2. The following data are obtained concerning R and D expenditures and sales for six health care firms
Firm 1 2 3 4 5 6
R and D (millions $), x 219 120 162 13 57 16
Sales (millions $), y 5,790 4,300 9,980 201 1,904 794
Construct a scatterplot for this data. What type of relationship do you see?
3. Find an example of two pairs of variables that are positively correlated. Give a reference for the source of data. Then, explain why you think they are positively correlated.
4. If a pair of variables show strong positive correlation, does this mean that one variable may be considered as a cause for the other? Explain your answer thoroughly and provide an example to illustrate your point.
5. Which of the following is true about the correlation measure r:
a) r can be any real number
b) r can be any positive real number
c) r is always between 0 and 1
d) r is always between 1 and 1
6. Provide a set of correlation values r that are consistent for the given phrase:
a) x and y have a strong positive correlation
b) x and y are not correlated
c) x and y show a mild negative correlation
7. a) Explain what a regression line is in terms of geometry.
b) What type of relationship should there be among two variables for a regression line to be used?
c) What are the advantages of regression?
8. Describe the two components of a one variable regression equation.
9. a) Explain what a residual is when developing a regression model.
b) Illustrate the concept of residuals using your scatterplot from Problem 2.
Part 2
1. The fleet manager of a trucking company is trying to improve his pricing policy and has been investigating the amount spent on gasoline. He would like to determine if there is a linear relationship between the weight of a loaded truck and gas mileage. The following information was collected where x is the weight of a loaded vehicle in hundreds of pounds and y is the miles per gallon.
x 26 35 29 39 20
y 22.0 16.1 18.8 15.7 23.4
a) Use SPSS or Excel to create a scatter plot for this data. Hint, use the Insert Menu for the scatterplot and Add Trend Line for the regression line. For additional help, see the website: http://www.excel-easy.com/examples/scatter-chart.html
b) Obtain the correlation for these two variables, display the regression line and the equation on the chart. Copy and paste the chart into your Word file.
c) If the weight of a vehicle is 32, what do you predict the gas mileage will be?
d) Should there be a gasoline surcharge for vehicles that weigh more than 3200 pounds? Justify you answer using the results of parts a, b, and c.
2. In Problem 3 of Part 2, Week 1 there are two data sets consisting of BMI and percent body fat. Perform a regression analysis to see if body fat percentage is a good predictor of BMI. Use SPSS or Excel and be sure to include the following:a) A scatterplot. Hint, use the Insert Menu for the scatterplot and Add Trend Line for the regression line. For additional help see the website http://www.excel-easy.com/examples/scatter-chart.html
b) A correlation measure r. Hint, use the Excel function CORREL
c) The graph of the regression line on the scatterplot Hint, Add a trend line to the Scatterplot
d) The regression equation. Hint, include the equation option when adding the trend line
e) A discussion that explains how well body fat works as a predictor of BMI
Copy and Paste the chart into your Word file.
3. In airplane manufacturing, rivets are used to join parts. The following table gives the number of oversize rivet holes and the number of minor repairs on 12 sections of an airplane.
Oversized Minor
Rivet Holes Repairs
46 22
52 26
48 21
60 28
67 33
61 32
70 33
54 25
52 34
67 35
48 26
57 30
a) Construct a scatterplot for this data.
b) Find the correlation measure r. for these two variables.
c) Add a regression line and regression equation to the scatterplot.
d) Use the results to discuss the relationship between these two variables.
e) Use the regression to predict the number of minor repairs when the number of oversized rivet holes is 40.
Copy and paste the Excel chart into your Word file.
Length: 5 – 7 pages
References: Include a minimum of two scholarly peer-reviewed resources.External Resource (S): Books and Resources for this Week
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