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Consider the following plot of two variables unemployment and underemployment in different years in the US.

Can I infer a positive correlation between unemployment and underemployment? For this purpose, I have usually seen scatter plots are used, but it seems that this plot also shows the correlation, right? enter image description here

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  • $\begingroup$ With a little practice you can learn to estimate the correlation coefficient accurately from a scatterplot. That's not possible with this pair of time series plots: typically, you should feel lucky to determine the sign of the correlation accurately from such plots. $\endgroup$ – whuber Feb 25 at 20:37
  • $\begingroup$ @whuber but they decrease and increase together, doesn't it mean a positive correlation? I'm not sure, what's the problem here. $\endgroup$ – Ahmad Feb 25 at 20:49
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    $\begingroup$ Yes--but can you reliably tell us what the correlation coefficient is from this plot? You could readily determine that from the scatterplot. $\endgroup$ – whuber Feb 25 at 20:50
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Before assessing your main question, we need to clarify some points:

1) inference is not the same thing of computing or showing the correlation;

2) since you are working with time series, you need to check if the series are both stationary or cointegrated; if it is not the case, you're correlation may be spurious and your conclusion, fallacious;

3) quantitative measures are in the vast majority of cases preferred to graphical methods; in the case of correlation, you should compute an appropriate coefficient rather than giving your conclusion using only a plot. After you have computed the coefficient, you should test if it is statistically significant.

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