TimescaleDB API referenceHyperfunctionsStatistical and regression analysis

Introduction

Perform linear regression analysis, for example to calculate correlation coefficient and covariance, on two-dimensional data. You can also calculate common statistics, such as average and standard deviation, on each dimension separately. These functions are similar to the PostgreSQL statistical aggregates, but they include more features and are easier to use in continuous aggregates and window functions. The linear regressions are based on the standard least-squares fitting method.

These functions work on two-dimensional data. To work with one-dimensional data, for example to calculate the average and standard deviation of a single variable, see the one-dimensional stats_agg functions.

Related hyperfunction groups

Aggregate

stats_agg (two variables)
Aggregate data into an intermediate statistical aggregate form for further calculation

Accessor

average_y, average_x
Calculate the average from a two-dimensional statistical aggregate for the dimension specified
corr
Calculate the correlation coefficient from a two-dimensional statistical aggregate
covariance
Calculate the covariance from a two-dimensional statistical aggregate
determination_coeff
Calculate the determination coefficient from a two-dimensional statistical aggregate
intercept
Calculate the intercept from a two-dimensional statistical aggregate
kurtosis_y, kurtosis_x
Calculate the kurtosis from a two-dimensional statistical aggregate for the dimension specified
num_vals
Calculate the number of values in a two-dimensional statistical aggregate
skewness_y, skewness_x
Calculate the skewness from a two-dimensional statistical aggregate for the dimension specified
slope
Calculate the slope from a two-dimensional statistical aggregate
stddev_y, stddev_x
Calculate the standard deviation from a two-dimensional statistical aggregate for the dimension specified
sum_y, sum_x
Calculate the sum from a two-dimensional statistical aggregate for the dimension specified
variance_y, variance_x
Calculate the variance from a two-dimensional statistical aggregate for the dimension specified
x_intercept
Calculate the x-intercept from a two-dimensional statistical aggregate

Rollup

rolling
Combine multiple two-dimensional statistical aggregates to calculate rolling window aggregates
rollup
Combine multiple two-dimensional statistical aggregates
stats_agg(
y DOUBLE PRECISION,
x DOUBLE PRECISION
) RETURNS StatsSummary2D

This is the first step for performing any statistical aggregate calculations on two-dimensional data. Use stats_agg to create an intermediate aggregate (StatsSummary2D) from your data. This intermediate form can then be used by one or more accessors in this group to compute the final results. Optionally, multiple such intermediate aggregate objects can be combined using rollup() or rolling() before an accessor is applied.

Required arguments
NameTypeDescription
y, xDOUBLE PRECISIONThe variables to use for the statistical aggregate.
Returns
ColumnTypeDescription
stats_aggStatsSummary2DThe statistical aggregate, containing data about the variables in an intermediate form. Pass the aggregate to accessor functions in the statistical aggregates API to perform final calculations. Or, pass the aggregate to rollup functions to combine multiple statistical aggregates into larger aggregates.
average_y(
summary StatsSummary 2D
) RETURNS DOUBLE PRECISION
average_x(
summary StatsSummary 2D
) RETURNS DOUBLE PRECISION

Calculate the average from a two-dimensional aggregate for the given dimension. For example, average_y() calculates the average for all the values of the y variable, independent of the values of the x variable.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
average_y, average_xDOUBLE PRECISIONThe average of the values in the statistical aggregate
Examples

Calculate the average of the integers from 0 to 100:

SELECT average_x(stats_agg(y, x))
FROM generate_series(1, 5) y,
generate_series(0, 100) x;
average
-----------
50
corr(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION

Calculate the correlation coefficient from a two-dimensional statistical aggregate. The calculation uses the standard least-squares fitting for linear regression.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
corrDOUBLE PRECISIONThe correlation coefficient of the least-squares fit line
Examples

Calculate the correlation coefficient of independent variable y and dependent variable x for each 15-minute time bucket:

SELECT
id,
time_bucket('15 min'::interval, ts) AS bucket,
corr(stats_agg(y, x)) AS summary
FROM foo
GROUP BY id, time_bucket('15 min'::interval, ts)
covariance(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION

Calculate the covariance from a two-dimensional statistical aggregate. The calculation uses the standard least-squares fitting for linear regression.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Optional arguments
NameTypeDescription
methodTEXTThe method used for calculating the covariance. The two options are population and sample, which can be abbreviated to pop or samp. Defaults to sample.
Returns
ColumnTypeDescription
covarianceDOUBLE PRECISIONThe covariance of the least-squares fit line
Examples

Calculate the covariance of independent variable y and dependent variable x for each 15-minute time bucket:

SELECT
id,
time_bucket('15 min'::interval, ts) AS bucket,
covariance(stats_agg(y, x)) AS summary
FROM foo
GROUP BY id, time_bucket('15 min'::interval, ts)
determination_coeff(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION

Calculate the determination coefficient from a two-dimensional statistical aggregate. The calculation uses the standard least-squares fitting for linear regression.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
determination_coeffDOUBLE PRECISIONThe determination coefficient of the least-squares fit line
Examples

Calculate the determination coefficient of independent variable y and dependent variable x for each 15-minute time bucket:

SELECT
id,
time_bucket('15 min'::interval, ts) AS bucket,
determination_coeff(stats_agg(y, x)) AS summary
FROM foo
GROUP BY id, time_bucket('15 min'::interval, ts)
intercept(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION

Calculate the y intercept from a two-dimensional statistical aggregate. The calculation uses the standard least-squares fitting for linear regression.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
interceptDOUBLE PRECISIONThe y intercept of the least-squares fit line
Examples

Calculate the y intercept from independent variable y and dependent variable x for each 15-minute time bucket:

SELECT
id,
time_bucket('15 min'::interval, ts) AS bucket,
intercept(stats_agg(y, x)) AS summary
FROM foo
GROUP BY id, time_bucket('15 min'::interval, ts)
kurtosis_y(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION
kurtosis_x(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION

Calculate the kurtosis from a two-dimensional statistical aggregate for the given dimension. For example, kurtosis_y() calculates the kurtosis for all the values of the y variable, independent of values of the x variable. The kurtosis is the fourth statistical moment. It is a measure of “tailedness” of a data distribution compared to a normal distribution.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Optional arguments
NameTypeDescription
methodTEXTThe method used for calculating the kurtosis. The two options are population and sample, which can be abbreviated to pop or samp. Defaults to sample.
Returns
ColumnTypeDescription
kurtosis_y, kurtosis_xDOUBLE PRECISIONThe kurtosis of the values in the statistical aggregate
Examples

Calculate the kurtosis of a sample containing the integers from 0 to 100:

SELECT kurtosis_y(stats_agg(data, data))
FROM generate_series(0, 100) data;
kurtosis_y
----------
1.78195
num_vals(
summary StatsSummary2D
) RETURNS BIGINT

Calculate the number of values contained in a two-dimensional statistical aggregate.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
num_valsDOUBLE PRECISIONThe number of values in the statistical aggregate
Examples

Calculate the number of values from 1 to 5, and from 0 to 100, inclusive:

SELECT num_vals(stats_agg(y, x))
FROM generate_series(1, 5) y,
generate_series(0, 100) x;
num_vals
--------
505
skewness_y(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION
skewness_x(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION

Calculate the skewness from a two-dimensional statistical aggregate for the given dimension. For example, skewness_y() calculates the skewness for all the values of the y variable, independent of values of the x variable. The skewness is the third statistical moment. It is a measure of asymmetry in a data distribution.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Optional arguments
NameTypeDescription
methodTEXTThe method used for calculating the skewness. The two options are population and sample, which can be abbreviated to pop or samp. Defaults to sample.
Returns
ColumnTypeDescription
skewness_y, skewness_xDOUBLE PRECISIONThe skewness of the values in the statistical aggregate
Examples

Calculate the skewness of a sample containing the integers from 0 to 100:

SELECT skewness_x(stats_agg(data, data))
FROM generate_series(0, 100) data;
skewness_x
----------
0
slope(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION

Calculate the slope of the linear fitting line from a two-dimensional statistical aggregate. The calculation uses the standard least-squares fitting for linear regression.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
slopeDOUBLE PRECISIONThe slope of the least-squares fit line
Examples

Calculate the slope from independent variable y and dependent variable x for each 15-minute time bucket:

SELECT
id,
time_bucket('15 min'::interval, ts) AS bucket,
slope(stats_agg(y, x)) AS summary
FROM foo
GROUP BY id, time_bucket('15 min'::interval, ts)
stddev_y(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION
stddev_x(summary
StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION

Calculate the standard deviation from a two-dimensional statistical aggregate for the given dimension. For example, stddev_y() calculates the skewness for all the values of the y variable, independent of values of the x variable.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Optional arguments
NameTypeDescription
methodTEXTThe method used for calculating the standard deviation. The two options are population and sample, which can be abbreviated to pop or samp. Defaults to sample.
Returns
ColumnTypeDescription
stddev_y, stddev_xDOUBLE PRECISIONThe standard deviation of the values in the statistical aggregate
Examples

Calculate the standard deviation of a sample containing the integers from 0 to 100:

SELECT stddev_y(stats_agg(data, data))
FROM generate_series(0, 100) data;
stddev_y
--------
29.3002
sum_y(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION
sum_x(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION

Calculate the sum from a two-dimensional statistical aggregate for the given dimension. For example, sum_y() calculates the skewness for all the values of the y variable, independent of values of the x variable.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
sumDOUBLE PRECISIONThe sum of the values in the statistical aggregate
Examples

Calculate the sum of the numbers from 0 to 100:

SELECT sum_y(stats_agg(data, data))
FROM generate_series(0, 100) data;
sum_y
-----
5050
variance_y(
summary StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION
variance_x(summary
StatsSummary2D,
[ method TEXT ]
) RETURNS DOUBLE PRECISION

Calculate the variance from a two-dimensional statistical aggregate for the given dimension. For example, variance_y() calculates the skewness for all the values of the y variable, independent of values of the x variable.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Optional arguments
NameTypeDescription
methodTEXTThe method used for calculating the standard deviation. The two options are population and sample, which can be abbreviated to pop or samp. Defaults to sample.
Returns
ColumnTypeDescription
varianceDOUBLE PRECISIONThe variance of the values in the statistical aggregate
Examples

Calculate the variance of a sample containing the integers from 0 to 100:

SELECT variance_y(stats_agg(data, data))
FROM generate_series(0, 100) data;
variance_y
----------
858.5
x_intercept(
summary StatsSummary2D
) RETURNS DOUBLE PRECISION

Calculate the x intercept from a two-dimensional statistical aggregate. The calculation uses the standard least-squares fitting for linear regression.

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
interceptDOUBLE PRECISIONThe x intercept of the least-squares fit line
Examples

Calculate the x intercept from independent variable y and dependent variable x for each 15-minute time bucket:

SELECT
id,
time_bucket('15 min'::interval, ts) AS bucket,
x_intercept(stats_agg(y, x)) AS summary
FROM foo
GROUP BY id, time_bucket('15 min'::interval, ts)
rolling(
ss StatsSummary2D
) RETURNS StatsSummary2D

Combine multiple intermediate two-dimensional statistical aggregate (StatsSummary2D) objects into a single StatsSummary2D object. It is optimized for use in a window function context for computing tumbling window statistical aggregates.

This is especially useful for computing tumbling window aggregates from a continuous aggregate. It can be orders of magnitude faster because it uses inverse transition and combine functions, with the possibility that bigger floating point errors can occur in unusual scenarios.

For re-aggregation in a non-window function context, such as combining hourly buckets into daily buckets, see rollup().

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
rollingStatsSummary2DA new statistical aggregate produced by combining the input statistical aggregates
rolling(
ss StatsSummary2D
) RETURNS StatsSummary2D

Combine multiple intermediate two-dimensional statistical aggregate (StatsSummary2D) objects into a single StatsSummary2D object. For example, you can use rollup to combine statistical aggregates from 15-minute buckets into daily buckets. For use in window function, see rolling().

Required arguments
NameTypeDescription
summaryStatsSummary2DThe statistical aggregate produced by a stats_agg call
Returns
ColumnTypeDescription
rollupStatsSummary2DA new statistical aggregate produced by combining the input statistical aggregates

Create a statistical aggregate that summarizes daily statistical data about two variables, val2 and val1, where val2 is the dependent variable and val1 is the independent variable. Use the statistical aggregate to calculate the average of the dependent variable and the slope of the linear-regression fit:

WITH t as (
SELECT
time_bucket('1 day'::interval, ts) as dt,
stats_agg(val2, val1) AS stats2D,
FROM foo
WHERE id = 'bar'
GROUP BY time_bucket('1 day'::interval, ts)
)
SELECT
average_x(stats2D),
slope(stats2D)
FROM t;

Keywords

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