Question 252425: Annual Income Level Amount Spent on Car
38,000 12,000
40,000 16,000
117,000 41,000
17,000 3,500
23,000 6,500
79,000 21,000
33,000 5,000
66,000 8,000
15,000 1,500
52,000 6,000
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.
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! 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.
ANSWER -> I would expect a positive correlation. The higher the income the more you would spend. It appears that the relationship will be fairly strong.
-----
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).
ANSWER -> First assume (X) is amount of money and (Y) is cost of car. If you have more money then it is reasonable to assume that you will spend more on a car. Second, assume (X) is cost of car and (Y) is amount of money. So I would say the directionality goes from earning more money to more expensive car. Interestingly enough, the correlation coefficient going both ways is the same at ~ .89
-----
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.
ANSWER -> AN ANOVA tests several variables against each other. You are trying to find strength of relationship between the variables. You could do this, but it wouldn't really make sense for just two variables - comparing one against the other. Regression models will be better here. You want to figure out if you make $X, then about how much will the car cost. A linear regression model is the best way to go. The correlation coefficient is ~ .89 [very strong].
|
|
|
