Discover Relationships Between Two Variables

Description Week 3 – Assignment: Discover Relationships Between Two Variables, write a paper that uses the following structure: • Begin with a one or two-paragraph introduction that summarizes the meaning of the reading material. • 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 why is the miles per gallon.