The coefficient of determination (
R2cap R squared
𝑅2
) measures the percentage of variance in a dependent variable explained by an independent
variable(s), ranging from 0 to 1 (0% to 100%). An
R2cap R squared
𝑅2
of
0.700.70
0.70
means
70%70 %
70%
of the data variation is explained by the model. It is calculated as
r2r squared
𝑟2
(square of the correlation coefficient) or
1−(Unexplained Variation/Total Variation)1 minus open paren Unexplained Variation /
Total Variation close paren
1−(Unexplained Variation/Total Variation)
.
Examples of
R2cap R squared
𝑅2
Interpretation

Study Time & Test Scores: If a model predicting test scores based on hours
studied has an
R2cap R squared
𝑅2
of
0.720.72
0.72
, this means
72%72 %
72%
of the variation in test scores is explained by study hours, while
28%28 %
28%
is due to other factors.

Plant Growth: A study investigating plant height relative to light intensity with an
R2cap R squared
𝑅2
of
0.640.64
0.64
indicates
64%64 %
64%
of the variation in plant height is explained by light, with
36%36 %
36%
explained by other factors.

Finance (Stock Market): An
R2cap R squared
𝑅2
of
0.3470.347
0.347
(or
34.7%34.7 %
34.7%
) indicates that a stock's price movements are somewhat, but not highly, correlated
with a benchmark index.

Environmental Science: A model showing
R2=0.68cap R squared equals 0.68
𝑅2=0.68
for skin cancer mortality rates based on latitude means
68%68 %
68%
of the variation in mortality rates is accounted for by, or "explained by," latitude.