The REGR_R2() aggregate function calculates the coefficient of determination (R2) for a linear regression model. The R2 value indicates how well the independent variable (x) explains the variability of the dependent variable (y).

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Syntax

The syntax for this function is as follows:

REGR_R2(y, x)

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Parameters

  • y: variable being predicted
  • x: variable used for prediction

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Example

For the needs of this section, we’re going to use a simplified version of the film table from the Pagila database, containing only the title, length and rating columns. The complete schema for the film table can be found on the Pagila database website.

DROP TABLE IF EXISTS film;
CREATE TABLE film (
  title text NOT NULL,
  rating int,
  length int
);
INSERT INTO film(title, length, rating) VALUES
  ('ATTRACTION NEWTON', 83, 5),
  ('CHRISTMAS MOONSHINE', 150, 7),
  ('DANGEROUS UPTOWN', 121, 4),
  ('KILL BROTHERHOOD', 54, 3),
  ('HALLOWEEN NUTS', 47, 5),
  ('HOURS RAGE', 122, 7),
  ('PIANIST OUTFIELD', 136, 7),
  ('PICKUP DRIVING', 77, 3),
  ('INDEPENDENCE HOTEL', 157, 7),
  ('PRIVATE DROP', 106, 4),
  ('SAINTS BRIDE', 125, 3),
  ('FOREVER CANDIDATE', 131, 7),
  ('MILLION ACE', 142, 5),
  ('SLEEPY JAPANESE', 137, 4),
  ('WRATH MILE', 176, 7),
  ('YOUTH KICK', 179, 7),
  ('CLOCKWORK PARADISE', 143, 5);

The query below uses the REGR_R2() function to calculate the coefficient of determination (R2) for valid pairs of rating and length:

SELECT
    REGR_R2(rating, length) AS coefficientOfDetermination
FROM film;

By running the above code, we’re going to get the following output:

 coefficientofdetermination 
----------------------------
         0.3832337818693347
(1 row)
REGR_INTERCEPTREGR_SLOPE