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Added Example for Statistical Functions in Docs #16927

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261 changes: 261 additions & 0 deletions docs/source/user-guide/sql/aggregate_functions.md
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Expand Up @@ -618,6 +618,36 @@ regr_avgx(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Exmaple

consider the following table:

```sql
> create table daily_sales(day int, temperature int) as values (1,35), (2,36), (3, NULL), (4,37), (5,38);
> select * from daily_sales;
+-----+-------------+
| day | total_sales |
| --- | ----------- |
| 1 | 100 |
| 2 | 150 |
| 3 | 200 |
| 4 | NULL |
| 5 | 250 |
+-----+-------------+
```

```sql
SELECT regr_avgx(total_sales, day) AS avg_day --considering day(x) independent variable
FROM daily_sales; --output = (1+2+3+5)/4 = 2.75
+----------+
| avg_day |
+----------+
| 2.75 |
+----------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_avgy`

Computes the average of the dependent variable (output) expression_y for the non-null paired data points.
Expand All @@ -631,6 +661,34 @@ regr_avgy(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

```sql
> create table daily_temperature(day int, temperature int) as values (1,30), (2,32), (3, NULL), (4,35), (5,36);
> select * from daily_temperature;
+-----+-------------+
| day | temperature |
| --- | ----------- |
| 1 | 30 |
| 2 | 32 |
| 3 | NULL |
| 4 | 35 |
| 5 | 36 |
+-----+-------------+
```

```sql
SELECT regr_avgy(temperature, day) AS avg_temperature --temperature as Dependent Variable(Y)
FROM daily_temperature;
+-----------------+
| avg_temperature |
+-----------------+
| 33.25 |
+-----------------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_count`

Counts the number of non-null paired data points.
Expand All @@ -644,6 +702,36 @@ regr_count(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

consider the following table:

```sql
> create table daily_metrics(day int, user_signups int) as values (1,100), (2,120), (3, NULL), (4,110), (5,NULL);
> select * from daily_metrics;
+-----+---------------+
| day | user_signups |
| --- | ------------- |
| 1 | 100 |
| 2 | 120 |
| 3 | NULL |
| 4 | 110 |
| 5 | NULL |
+-----+---------------+
```

```sql
SELECT regr_count(user_signups, day) AS valid_pairs
FROM daily_metrics;
+-------------+
| valid_pairs |
+-------------+
| 3 |
+-------------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_intercept`

Computes the y-intercept of the linear regression line. For the equation (y = kx + b), this function returns b.
Expand All @@ -657,6 +745,36 @@ regr_intercept(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

consider the following table:

```sql
>create table weekly_performances(week int, productivity_score int) as values (1,60), (2,65), (3, 70), (4,75), (5,80);
> select * from weekly_performances;
+------+---------------------+
| week | productivity_score |
| ---- | ------------------- |
| 1 | 60 |
| 2 | 65 |
| 3 | 70 |
| 4 | 75 |
| 5 | 80 |
+------+---------------------+
```

```sql
SELECT regr_intercept(productivity_score, week) AS intercept
FROM weekly_performance;
+----------+
|intercept |
+----------+
| 55 |
+----------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_r2`

Computes the square of the correlation coefficient between the independent and dependent variables.
Expand All @@ -670,6 +788,36 @@ regr_r2(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

consider the following table:

```sql
>create table weekly_performances(day int ,user_signups int) as values (1,60), (2,65), (3, 70), (4,75), (5,80);
> select * from weekly_performances;
+------+---------------------+
| week | productivity_score |
| ---- | ------------------- |
| 1 | 60 |
| 2 | 65 |
| 3 | 70 |
| 4 | 75 |
| 5 | 80 |
+------+---------------------+
```

```sql
SELECT regr_r2(productivity_score, week) AS r_squared
FROM weekly_performance;
+---------+
|r_squared|
+---------+
| 1.0 |
+---------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_slope`

Returns the slope of the linear regression line for non-null pairs in aggregate columns. Given input column Y and X: regr_slope(Y, X) returns the slope (k in Y = k\*X + b) using minimal RSS fitting.
Expand All @@ -683,6 +831,37 @@ regr_slope(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

```sql
>create table weekly_performances(day int,user_signups int) as values (1,60), (2,65), (3, 70), (4,75), (5,80);
> select * from weekly_performances;
+------+---------------------+
| week | productivity_score |
| ---- | ------------------- |
| 1 | 60 |
| 2 | 65 |
| 3 | 70 |
| 4 | 75 |
| 5 | 80 |
+------+---------------------+
```

```sql
--in simpler words slope = Δx/Δy
SELECT regr_slope(productivity_score, week) AS slope
FROM weekly_performance;
+--------+
| slope |
+--------+
| 5.0 |
+--------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

**Remember**: the slops tells _how much y changes when x increases by 1._

### `regr_sxx`

Computes the sum of squares of the independent variable.
Expand All @@ -696,6 +875,36 @@ regr_sxx(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

consider the following table `study_hours`:

```sql
> crate table study_hours(int student_id, int hours,int test_score) as values(1,2,55),(2,4,65) , (3,6,75),(4,8,85),(5,10,95);
>select * from study_hours;
+-------------+-----------+-----------------+
| student_id | hours (x) | test_score (y) |
| ----------- | --------- | --------------- |
| 1 | 2 | 55 |
| 2 | 4 | 65 |
| 3 | 6 | 75 |
| 4 | 8 | 85 |
| 5 | 10 | 95 |
+-------------+-----------+-----------------+
```

```sql
SELECT regr_sxx(test_score, hours) AS sxx
FROM study_hours; --Output - 40
+-------+
| sxx |
+-------+
| 40 |
+-------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_sxy`

Computes the sum of products of paired data points.
Expand All @@ -709,6 +918,32 @@ regr_sxy(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

```sql
> create table employee_productivity(int week,int productivity_score) as values(1,60) , (2,65), (3,70);
>select * from employee_productivity;
+-------+---------------------+
| week | Procutivity_score |
+-------+---------------------+
| 1 | 65 |
| 2 | 70 |
| 3 | 75 |
+-------+---------------------+
```

```sql
SELECT regr_sxy(productivity_score, week) AS sum_product_deviations
FROM employee_productivity;
+------------------------+
| sum_product_deviations |
+------------------------+
| 10.0 |
+------------------------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `regr_syy`

Computes the sum of squares of the dependent variable.
Expand All @@ -722,6 +957,32 @@ regr_syy(expression_y, expression_x)
- **expression_y**: Dependent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.
- **expression_x**: Independent variable expression to operate on. Can be a constant, column, or function, and any combination of operators.

### Example

```sql
> create table employee_productivity(int week,int productivity_score) as values(1,60) , (2,65), (3,70);
>select * from employee_productivity;
+-------+---------------------+
| week | Procutivity_score |
+-------+---------------------+
| 1 | 65 |
| 2 | 70 |
| 3 | 75 |
+-------+---------------------+
```

```sql
SELECT regr_syy(productivity_score, week) AS sum_squares_y
FROM employee_productivity;
+---------------+
| sum_squares_y |
+---------------+
| 50.0 |
+---------------+
1 row(s) fetched.
Elapsed 0.001 seconds.
```

### `stddev`

Returns the standard deviation of a set of numbers.
Expand Down