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Cars and Income: Estimation of Correlation

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 $10,000
$40,000 $14,000
$117,000 $37,000
$17,000 $2,500
$23,000 $6,000
$79,000 $18,000
$33,000 $4,000
$66,000 $5,000
$15,000 $1,000
$52,000 $5,000

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, http://people.hofstra.edu/Stefan_Waner/newgraph/regressionframes.html 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.

Solution Preview

See the attached file as it contains graph. The text below is also included in the Word file:

Problem:

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 $10,000
$40,000 $14,000
$117,000 $37,000
$17,000 $2,500
$23,000 $6,000
$79,000 $18,000
$33,000 $4,000
$66,000 $5,000
$15,000 $1,000
$52,000 $5,000

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 ...

Solution Summary

The solution provides detailed explanations on why some correlation between cars and annual income is expected, the sign of this correlation and the strength of this relationship. It also discusses the likely causality between the two variables and justifies choice of an appropriate statistical technique (ANOVA vs. simple regression).

Finally, calculations and a graph are provided and discussed.

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