# Regression Correlation Using a Data Set

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

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 (http://people.hofstra.edu/faculty/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.

https://brainmass.com/math/interpolation-extrapolation-and-regression/regression-correlation-using-a-data-set-127789

#### Solution Preview

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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 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

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.

I would expect that there is a positive correlation between annual income and amount spent on car (the higher the income, the more spent on car, and vice versa).

This is intuitive, since if you don't make much money, you can't spend much on a car, and if you have a lot of money, you can afford to spend a lot on a car, and you might want a more expensive car as a status symbol. A look at the data confirms this (the people with the ...