Question

Suppose I do a correlational study on variable X and Y. After doing statistical analysis, I find that X and Y have a - .91 correlation. What does this mean? And is the a strong correlation? Why or why not?

Answer 1

The correlational study on variable X and Y is actually a degree of association between these two random variable X and Y. If we see the correlation formula,

The correlation is the division of covariance of X, Y and standard deviation of X multiplied by standard deviation of Y. So the covarince is normalizing with respect to the standard deviation of X and standard deviation of Y. The value of correlation coefficient varies between -1 and +1

If the variable X and Y are independent which means covariance between X and Y will be 0 therefore, the correlation will be 0.

If the correlation coefficient value is +1, then we have a perfect positive correlation. The screenshot for perfect positive correlation is shown below,

If the correlation coefficient value is -1, then we have a negative correlation. The screenshot for perfect negative correlation is shown below,

If the correlation coefficient value less than +0.3 (-0.3 for negative correlation), then we have a weak correlation. The screenhot is shown below for weak positive correlation,

If the correlation coefficient value is between +0.3 and +0.7 (-0.3 and -0.7 for negative correlation), then we have a moderate correlation. The screenhot for moderate positive correlation is shown below,

If the correlation coefficient value is between above +0.7 (-0.7 for negative correlation), then we have a strong correlation. The screenhot for strong positive correlation is shown below,