Question

Why is it advisable to generate a scatterplot before computing a correlation coefficient between two variables? Describe how a scatterplot might differ when viewing correlations that represent positive, negative, and no relationship between predictor and criterion variables. Is it possible to have a relation between variables that systematic (i.e., reliable and predictable) yet not linear?

Answer 1

It is advisable to generate a scatterplot before computing a correlation coefficient between two variables as it shows visually the relationship between the two variables and whether there is a linear relationship between the two variables or not. Depending on the kind of relationship between the variables i.e, linear or nonlinear-  it is then decided which statistical measure would be suitable to calculate the correlation between the variables.

When the variables increase and decrease together and at a constant rate, a positive linear relationship exists and the scatterplot shows the data points as shown in figure:

If one variable tends to increase as the other decreases , the relationship is negative as shown below:

If there is no relationship, the scatterplot depicts no pattern among the data points.

Yes, it is possible to have a relationship that is systematic yet not linear. When the variables increase or decrease at a different rate then we get a relationship that is depicted by a curve which is nonlinear.