Scatter Diagram

A third graph is the scatter diagram, the graph that, for reasons unknown to me, seems over the years to have caused students the most problems. It need not be this way since there is nothing particularly difficult about the construction or interpretation of scatter graphs. They are designed to provide the viewer with a visual image of the nature of a relationship between any two phenomena. To better see how to construct and interpret the graphs, assume that you have decided to undertake a study to determine the relationship between two phenomena, X and Y. As a first step, you have collected eight observations on the variables for the years 1981 through 1988. Some important relationships from your Economics courses which you might have wanted to explore would be the relationships between consumption spending and income, quantity demanded and price, exchange rates and imports, inflation and unemployment, or the budget and trade deficits. What you want to know is whether or not these data support the hypothesis that there is a relationship between y and x?

Below you will find four possible 'patterns' that could emerge from your analysis. In each diagram the points correspond to the individual years with the point corresponding to 1983 having been marked in each diagram. What you are looking for is a pattern. Is there some line that I could draw so that the scatter of points would be clustered around the line? If so, we have found some evidence of a relationship between x and y. In the first diagram the points tend to be loosely scattered around the positively sloped line, while in the second diagram the points seem to be more tightly packed around the negatively sloped line. Based on these findings we would be led to conclude in case a. that there is weak evidence that y and x are positively related while in b. there is strong evidence of a negative relationship. In diagram c, where the scatter of points resembles the scatter of darts thrown by a novice, there is little evidence of any relationship as the points seem to be randomly distributed. Finally, in diagram d, the data suggests that there is evidence of a positive relationship between y and x, but it a nonlinear relationship, the type that we would expect in a study of the income-consumption spending relationship.

Before leaving scatter diagrams behind, let us turn to the specific problem of determining the relationship between the inflation rate and interest rates. Economic theory leads you to believe that interest rates (r) and inflation rates (i) are positively related, an increase in inflation rates pushing up interest rates. To test this theory the data on interest rates and inflation that appear in the accompanying table were collected. Do these data support the hypothesis that there is a relationship between interest rates and inflation?

The scatter diagram generated by these data is presented below where once again each point represents one year. For example, the highest point on the Inflation and Interest Rate scatter diagram below corresponds to 1981 when the interest rate was 14 percent and the inflation rate was 10.3 percent. As you can see, there does tend to be a relationship between the two variables. The scatter of points tends to rise as we move to the right; as i increases, r tends to increase, but certainly not in a way that can be easily captured by some linear relationship. This is where you would need to call on some of the techniques that you learned in statistics, but we will leave that for a later date.