# Is this a correct interpretation of the r correlation coefficient

According to this site, which is a top google search site, "The higher the coefficient, the higher percentage of points the line passes through when the data points and line are plotted. If the coefficient is 0.80, then 80% of the points should fall within the regression line. " Is this true? Does $$100r$$ value give us the percentage of points that lie on a linear regression curve.

On another site I see the image I posted below, and it shows very few points that lie on the line of best fit , but the $$r$$ value which is about 0.95 is relatively high.

• It sure looks like the line misses a lot more than 8% of the points in your plot! We wouldn’t expect any of the points to be right on the regression line, in fact.
– Dave
Nov 20 '19 at 4:52
• What a piece of utter nonsense. You should not trust the drivel that Google searches turn up. There's a saying "on the internet nobody knows you're a dog", but apparently there's a few out there giving the game away. Nov 20 '19 at 6:33
• @Glen_b-ReinstateMonica quick question, is it called R pearson correlation coefficient or R spearman correlation coefficient.
– john
Nov 21 '19 at 5:35
• The relevant correlation measure for the usual least squares regression line is the Pearson correlation, which is typically denoted r (for a sample correlation at least). In simple regression (one predictor) its also equal to R, which is the correlation between the data and the fitted values. Nov 21 '19 at 8:22
• As other users have pointed out, that is not actually the correct interpretation of the $R^2$ coefficient in a linear regression. However, in the particular case of the plot you have included, there are much bigger problems, since the person that created it is trying to fit a straight line through a time-series that is clearly exponential in nature. Population growth over time tends to involve fluctuation in its growth rate, which operates on the existing population in a multiplicative way. Therefore, it is generally best to model it with an auto-regressive model operating on the logarithms
– Ben
Nov 21 '19 at 10:27

## 1 Answer

An r of .8 does NOT mean the line goes through 80% of the data points. It means the points are tightly clustered around a line, but it may not go through any of them. The sign of r indicates if the association between the x and y variables is positive or negative, and the square of r gives a measure of what percent of the variability of the data is explained by a linear model.

• quick question, is it called R pearson correlation coefficient or R spearman correlation coefficien
– john
Nov 21 '19 at 5:36
• I think both Pearson's and Spearman's correlations are denoted with an "r", but i think generally people means Pearson's if they don't specify. Nov 28 '19 at 15:02