> ## Documentation Index
> Fetch the complete documentation index at: https://mintlify-poc.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Statistical and regression analysis overview

> Functions for statistical analysis and linear regression on time-series data

Perform statistical analysis and linear regression on time-series data. These functions are similar to PostgreSQL
statistical aggregates, but they include more features and are easier to use in continuous aggregates and window
functions.

## Two-step aggregation

This group of functions uses the two-step aggregation pattern.

Rather than calculating the final result in one step, you first create an
intermediate aggregate by using the aggregate function.

Then, use any of the accessors on the intermediate aggregate to calculate a
final result. You can also roll up multiple intermediate aggregates with the
rollup functions.

The two-step aggregation pattern has several advantages:

1. More efficient because multiple accessors can reuse the same aggregate
2. Easier to reason about performance, because aggregation is separate from
   final computation
3. Easier to understand when calculations can be rolled up into larger
   intervals, especially in window functions and continuous aggregates
4. Perform retrospective analysis even when underlying data is dropped, because
   the intermediate aggregate stores extra information not available in the
   final result

To learn more, see the [blog post on two-step aggregates][blog-two-step-aggregates].

[blog-two-step-aggregates]: https://www.timescale.com/blog/how-postgresql-aggregation-works-and-how-it-inspired-our-hyperfunctions-design

## Samples

### One-dimensional statistical analysis

Calculate the average, standard deviation, and skewness of daily temperature readings:

```sql theme={"dark"}
WITH daily_stats AS (
    SELECT
        time_bucket('1 day'::interval, time) AS day,
        stats_agg(temperature) AS stats
    FROM weather_data
    GROUP BY day
)
SELECT
    day,
    average(stats) AS avg_temp,
    stddev(stats) AS std_dev,
    skewness(stats) AS skew
FROM daily_stats
ORDER BY day;
```

### Two-dimensional regression analysis

Calculate the correlation coefficient and linear regression slope between two variables:

```sql theme={"dark"}
WITH daily_stats AS (
    SELECT
        time_bucket('1 day'::interval, time) AS day,
        stats_agg(sales, temperature) AS stats
    FROM store_data
    GROUP BY day
)
SELECT
    day,
    corr(stats) AS correlation,
    slope(stats) AS regression_slope,
    intercept(stats) AS y_intercept
FROM daily_stats
ORDER BY day;
```

### Rolling window calculations

Calculate a 7-day rolling average using the rolling window function:

```sql theme={"dark"}
SELECT
    time_bucket('1 day'::interval, time) AS day,
    average(rolling(stats_agg(temperature)) OVER (ORDER BY time_bucket('1 day'::interval, time) ROWS 6 PRECEDING)) AS rolling_avg_7day
FROM weather_data
GROUP BY day
ORDER BY day;
```

## Available functions

### One-dimensional statistics

* [`stats_agg() (one variable)`][stats_agg-one-variable]: analyze statistical properties of a single variable

### Two-dimensional statistics and regression

* [`stats_agg() (two variables)`][stats_agg-two-variables]: analyze statistical properties and linear regression of two
  variables

[stats_agg-one-variable]: /api-reference/timescaledb-toolkit/statistical-and-regression-analysis/stats_agg-one-variable

[stats_agg-two-variables]: /api-reference/timescaledb-toolkit/statistical-and-regression-analysis/stats_agg-two-variables

[toolkit-1.3.0]: https://github.com/timescale/timescaledb-toolkit/releases/tag/1.3.0

[two-step-aggregation]: #two-step-aggregation