# regr_sxx

Calculates the sum of squared deviations of the independent variable.

This is the denominator used by `regr_slope`. It is zero when every admitted `x` value is the same.

**Syntax**

```text
regr_sxx(y, x)
```

**Arguments**

* `y` — The dependent numeric variable.
* `x` — The independent numeric variable.

A row contributes only when both arguments are non-`NULL`. The means and the count in the formulas below use these complete pairs, rather than each column separately.

**Calculation**

```text
Sxx = sum((x - mean_x) * (x - mean_x))
```

Here `n` is the number of complete pairs, `mean_x` and `mean_y` are their arithmetic means, `Sxx` and `Syy` are their centered sums of squares, and `Sxy` is their centered cross-product sum.

**Returned value**

The nonnegative centered sum of squares as `REAL`. No complete pairs returns `NULL`; one complete pair returns `0.0`.

The result is approximate, including when the inputs are exact integers or decimals. Nonfinite inputs return `NULL`; finite arithmetic overflow raises `NUMERIC_OVERFLOW`.

**Examples**

**Measurements with a linear relationship**

The complete observations below follow `reading = 2 * hour + 1`. The two incomplete observations are excluded.

```sql
CREATE TABLE measurements (hour INTEGER, reading INTEGER);
INSERT INTO measurements VALUES (1, 3), (2, 5), (3, 7), (4, 9), (5, NULL), (NULL, 100);
```

```sql
SELECT round(regr_sxx(reading, hour), 6) AS result
FROM measurements
FORMAT csv;
```

```text
5.0
```

**No complete observations**

```sql
CREATE TABLE incomplete_measurements (hour INTEGER, reading INTEGER);
INSERT INTO incomplete_measurements VALUES (1, NULL), (NULL, 5);
```

```sql
SELECT regr_sxx(reading, hour)
FROM incomplete_measurements
FORMAT csv;
```

```text
\N
```

**Related functions**

* [`regr_count`](https://coordinatordb.com/docs/reference/functions/aggregate-functions/regr-count) counts the pairs used by the calculation.
* [`regr_slope`](https://coordinatordb.com/docs/reference/functions/aggregate-functions/regr-slope) and [`regr_intercept`](https://coordinatordb.com/docs/reference/functions/aggregate-functions/regr-intercept) describe the fitted line.
* [`covar_pop`](https://coordinatordb.com/docs/reference/functions/aggregate-functions/covar-pop), [`covar_samp`](https://coordinatordb.com/docs/reference/functions/aggregate-functions/covar-samp) and [`corr`](https://coordinatordb.com/docs/reference/functions/aggregate-functions/corr) describe the relationship between the variables.