### MAT 101 Case

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Look at the data below for the income levels and prices paid for cars for ten people:

Annual Income Level

Amount Spent on Car

38,000

40,000

117,000

17,000

23,000

79,000

33,000

66,000

15,000

52,000

12,000

16,000

41,000

3,500

6,500

21,000

5,000

8,000

1,500

6,000

Answer the following questions:

A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking through the data.

B. What is the direction of causality in this relationship - i.e. does having a more expensive car make you earn more money, or does earning more money make you spend more on your car? In other words, define one of these variables as your dependent variable (Y) and one as your independent variable (X).

C. What method do you think would be best for testing the relationship between your dependent and independent variable, ANOVA or regression? Explain your reasoning thoroughly with a discussion of both methods.

D. Go to this calculation page and enter in your data in the X and Y columns (don't use commas, enter 8,000 as 8000). Then click on the button "Y=MX B". Then click on the "graph" button. Write out your equation as calculated, along with your coefficients. Discuss the significance and interpretation of this result, and discuss your graph.

Case assignment expectations:

Use information from the modular background readings as well as any good quality resource you can find. Please cite all sources and provide a reference list at the end of your paper.

The following items will be assessed in particular:

1. Your ability to explain the limitations of the linear regression method.

2. Your ability to describe ANOVA and identify when the ANOVA method should be used.

3. Your ability to describe the correlation analysis and identify when the coefficient of correlation should be calculated.

4. Your ability to identify when the Least Squares method should be used.

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