Add compensation integration (#15192)

Co-authored-by: Klaas Schoute <klaas_schoute@hotmail.com>
Co-authored-by: Franck Nijhof <frenck@frenck.nl>

source/_integrations/compensation.markdown

@@ -0,0 +1,62 @@
+---
+title: Compensation
+description: Instructions on how to integrate compensation sensors into Home Assistant.
+ha_category:
+  - Utility
+  - Sensor
+ha_iot_class: Calculated
+ha_release: "2021.5"
+ha_quality_scale: internal
+ha_codeowners:
+  - '@petro31'
+ha_domain: compensation
+---
+
+The Compensation integration consumes the state from other sensors. It exports the compensated value as state and the following values as attributes: `entity_id` and `coefficients`.  A single polynomial, linear by default, is fit to all data points provided.
+
+## Configuration
+
+To enable the compensation sensor, add the following lines to your `configuration.yaml`:
+
+```yaml
+# Example configuration.yaml entry
+compensation:
+  media_player_db_volume:
+    source: media_player.yamaha_receiver
+    data_points:
+      - [0.2, -80.0]
+      - [1.0, 0.0]
+```
+
+{% configuration %}
+source:
+  description: The entity to monitor.
+  required: true
+  type: string
+data_points:
+  description: "The collection of data point conversions with the format `[uncompensated_value, compensated_value]`.  e.g., `[1.0, 2.1]`. The number of required data points is equal to the polynomial `degree` + 1. For example, a linear compensation (with `degree: 1`) requires at least 2 data points."
+  required: true
+  type: list
+unique_id:
+  description: An ID that uniquely identifies this sensor. Set this to a unique value to allow customization through the UI.
+  required: false
+  type: string
+attribute:
+  description: Attribute to monitor.
+  required: false
+  type: string
+degree:
+  description: "The degree of a polynomial. e.g., Linear compensation (y = x + 3) has 1 degree, Quadratic compensation (y = x<sup>2</sup> + x + 3) has 2 degrees, etc."
+  required: false
+  default: 1
+  type: integer
+precision:
+  description: Defines the precision of the calculated values, through the argument of round().
+  required: false
+  default: 2
+  type: integer
+unit_of_measurement:
+  description: Defines the units of measurement of the sensor, if any.
+  required: false
+  type: string
+{% endconfiguration %}