In other words, they are positively correlated. However, it is important to note that some of the data indicate that at some levels of income ($ 52,000 and $ 66,000), the amount spent on cars decrease when compared to lower levels ($ 38,000 and $ 40,000). There are a few more values which differ from the rest. However, most of the data indicate that the relationship is positive.
The Correlation coefficient is positive confirming the positive association between the two variables. Also, the value of the coefficient is 0.89 which indicates a strong relationship between the two variables.
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).
In order to identify the direction of causality, the two variables are analyzed objectively. When a person spends more money on the car, it does not have any effect on his income. Hence it is evident that the amount spent on the car does not affect or have an influence on the annual income of the person. However, when a person’s annual income increases, he is more likely to spend higher on the car. In other words, annual income is the cause and the amount spent on car is the effect. Hence the annual income is the independent variable (X) and the amount spent on the car is the dependent variable (Y). The amount spent on the car (Y) depends on the annual income (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.
Correlation establishes the association between two variables, however does not indicate the direction of causation