Statistics Question

Question

b) Characterize the correlation.

Answer 1

There are several ways of characterizing this. One is the consider how well the line matches the data points. In this case, the points are not really very close to the line, evident by the R² value of 0.1524. Generally, the closer the R² is to the number "1", the better the fit. But you can categorize the fit approximately like this:

R² = 1: Perfect fit. Every point is on the Least Squares Regression (best-fit) Line

0.8 < R² < 1: Strong fit. Data points are strongly close to the LSR Line

0.6 < R² < 0.8: Moderately strong fit. Data points are moderately close to the LSR Line

0.4 < R² < 0.6: Moderate fit. Data points are close to the LSR Line

0.2 < R² < 0.4: Mild fit. Data points are mildly close to the LSR Line

0 < R² < 0.2: Weak or no fit. There is little or no relationship between the data points and the LSR Line

We could say for this case that the data points have a weak linear correlation.

You can also characterize the correlation as either positive or negative. If the data values (dependent variable) increase as the independent variable increases (positive slope), then there is a positive correlation. If the data decreases as the independent variable increases (negative slope), then there is a negative correlation.

So, I would say this data has a weak positive correlation. Note that the number ranges are subjective and dependent on other conditions as well. It could easily be argued that this data has a mild or even moderate positive correlation.