Question

The correlation coefficient between two quantitative variables is approximately 0.02. What does the value of this correlation coefficient indicate about how well the model fits the data?

Answer 1

The correlation coefficient "tell us" that the model in question does not fit the data well (the correlation coefficient is near zero), in whose case we need to find another that can do it.

Explanation:

Roughly speaking, the correlation coefficient "tell us" if two variables could present the following behavior:

1. As one variable increases, the other variable increases too. In this case, the correlation coefficient is high and positively correlated. As the correlation coefficient is near 1, the correlation between two quantitative variables is almost perfect.
2. As one variable decreases, the other variable decreases too. In this case, the correlation coefficient is also high, but negatively correlated. As the correlation coefficient is near -1, this correlation is almost perfect for this case.
3. There could be no correlation at all. In this case, the correlation coefficient is near a zero value.

As we can follow from the question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.

Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it. For example, if the model is linear, we need to test an exponential model.

It is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.