Interpreting Correlation and Scatter Plot Results

Question

I tested for correlation between average unemployment rate and log average real GDP (U.S. 2017 dollars) for 163 countries, and created the scatter plot below:

Based on the correlation coefficient and the scatter plot, is it fair to say that there is a small yet positive correlation between the two variables?

I am a bit puzzled as I expected a negative correlation where unemployment rate declines as log GDP rises.. However, I also understand that the relationship may go in the opposite direction where in low-income countries, people may have a greater incentive to work, and thus lower unemployment rate.

Is my reading of the scatter plot and correlation coefficient correct?

corr avg_unemp log_avg_gdp
(obs=163)

             | avg_un~p log_av~p
-------------+------------------
   avg_unemp |   1.0000
 log_avg_gdp |   0.0177   1.0000

Answer 1

Your point estimate of the correlation coefficient is indeed very small, so you might do well to perform a hypothesis test to see if it is significantly different from zero. It's possible that the true correlation value is actually zero (no correlation whatsoever), and that your non-zero correlation coefficient is simply a result of statistical noise. Even if you had many more samples and found that the correlation of 0.02 was significantly different from zero, you can also ask whether that is a meaningful finding. At this correlation level, changes in GDP explain only about three hundredths of a percent of the variation in unemployment - is that useful to you?

I think the scatter plot is also quite informative, as it seems you do not have one fixed linear relationship across the entire domain of GDPs. With this observation, you may want to step back and consider whether it makes sense to try to describe the GDP-unemployment relationship with one single number, or if that relationship will depend on GDP itself, as you suggest.