Problem 55225. Simpson's Paradox - Calculate correlation coefficients for groups of data

Simpson's Paradox is a statistical phenomenon where groups of data can have a characteristic while the whole data set together has the opposite characteristic. In the example below, both groups have a negative correlation between x and y, but collectively there is a positive correlation.
A scatter plot of blue and orange points. The blue points are near the origin and appear negatively correlated. The orange points are further from the origin and also negatively correlated. Best fit lines go through each group separately. Correlation coefficients of r = -0.68 and r = -0.44, respectively, are shown. A black best fit line is shown for all the data. It has positive slope. The correlation coefficient is r = 0.88
Write a function that takes three vectors as input: x, y, and g. The vector g will contain only the values 1 and 2. The function should return three outputs. These outputs are the Pearson correlation coefficients for three different groupings of the data, which are: (1) for all x and y, (2) x and y corresponding to elements where g has the value 1, (3) x and y for which g is 2.
[c,c1,c2] = groupcorr(x,y,g)
c =
0.8800
c1 =
-0.6800
c2 =
-0.4396
Solve

Solution Stats

39.55% Correct | 60.45% Incorrect
Last Solution submitted on Apr 22, 2025

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