Analysis techniques and correlation methods

Mathematics

Analysis Techniques: Correlation

A positive correlation between annual income and amount spent on car would be expected. This means that there is a relationship between the two and that, in general, higher annual income would show an increase in the amount spent on car, while lower annual income would show a decrease in the amount spent on car.

However, it would not be expected that this would be a strong relationship because other factors would influence the amount spent on car. For example, some individuals with an income in the middle range may consider an expensive car a key priority, while others would have other priorities. In addition, annual income level is not a true measure of wealth because it does not take into account a person's expenses. For example, a young single person without a family and without a mortgage would have more disposable income than a married person with four children and a mortgage. These other considerations suggest that there will be a general trend showing that higher income level shows an increase in the amount spent on car. However, other factors would make this a weak correlation.

A consideration of the data also suggests a weak correlation. It can be seen that there is a general trend toward annual income level increasing the amount spent on a car. This is especially seen with the lowest income and the highest income. However, there are also exceptions to the trend, with a lot of variation seen in the middle-income levels.

B.

The direction of causality is that earning more money makes you spend more on your car, not that having a more expensive car makes you earn more money. Therefore, amount spent on car is the dependant variable (Y), and annual income level is the independent variable (X).

C.

Data:

Annual Income Level ($)

Amount Spent on Car ($)

Regression Calculation:

Regression Output:

Constant

-3996.77843523997

Std Err of Y Est

Squared

No. Of Observations

Degrees of Freedom

Coefficient(s)

Std Err of Coef.

Regression coefficient = 0.67

The regression coefficient of 0.67 shows that there is a positive correlation between annual income level and amount spent on car. This is as was expected. The graph also illustrates the general trend of increasing income level resulting in an increase in the amount spent on car.