Deterministic statistics over (x, y) points

Deterministic statistics over (x, y) points: ordinary least squares linear regression with standard errors and confidence intervals, a fitted normal distribution with quantiles and probability queries, exact Student t and Jarque-Bera p-values validated at your alpha, and predictions with prediction intervals. Points come inline or from a BigQuery table (two numeric columns; above max_rows the rows are chosen by fingerprint, never at random).

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Endpoint

POST https://hubvibe-io.com/work/stats/probability

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Example input (from the provider)

{
  "body": {
    "points": [
      [
        1,
        2.1
      ],
      [
        2,
        3.9
      ],
      [
        3,
        6.2
      ],
      [
        4,
        7.8
      ],
      [
        5,
        10.1
      ]
    ],
    "predict_x": [
      6
    ],
    "probability_queries": [
      {
        "below": 8
      }
    ]
  },
  "bodyType": "json",
  "method": "POST",
  "type": "http"
}

Promised output schema (from the provider)

{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "properties": {
    "input": {
      "additionalProperties": false,
      "properties": {
        "body": {
          "additionalProperties": false,
          "oneOf": [
            {
              "required": [
                "points"
              ]
            },
            {
              "required": [
                "table",
                "x_column",
                "y_column"
              ]
            }
          ],
          "properties": {
            "alpha": {
              "description": "Significance level for p-value validation and intervals. Default 0.05.",
              "exclusiveMaximum": 1,
              "exclusiveMinimum": 0,
              "type": "number"
            },
            "distribution_of": {
              "description": "Which values the normal model fits. Default y.",
              "enum": [
                "y",
                "x",
                "residuals"
              ],
              "type": "string"
            },
            "max_rows": {
              "description": "Rows to read from `table`, default 10000. A larger table is reduced to this many rows by FARM_FINGERPRINT order, so the same table always yields the same rows.",
              "maximum": 100000,
              "minimum": 3,
              "type": "integer"
            },
            "metrics": {
              "description": "Which results to compute. Default: linear_regression, normal_distribution and p_values, plus prediction when predict_x is given.",
              "items": {
                "enum": [
                  "linear_regression",
                  "normal_distribution",
                  "p_values",
                  "prediction"
                ],
                "type": "string"
              },
              "minItems": 1,
              "type": "array",
              "uniqueItems": true
            },
            "points": {
              "description": "The data: [x, y] pairs (or {x, y} objects), 2 to 100000 of them; at least 3 for a regression. Use this OR `table`.",
              "items": {
                "oneOf": [
                  {
                    "description": "[x, y]",
                    "items": {
                      "type": "number"
                    },
                    "maxItems": 2,
                    "minItems": 2,
                    "type": "array"
                  },
                  {
                    "additionalProperties": false,
                    "properties": {
                      "x": {
                        "type": "number"
                      },
                      "y": {
                        "type": "number"
                      }
                    },
                    "required": [
                      "x",
                      "y"
                    ],
                    "type": "object"
                  }
                ]
              },
              "maxItems": 100000,
              "minItems": 2,
              "type": "array"
            },
            "predict_x": {
              "description": "x values to predict y at, with mean and prediction intervals.",
              "items": {
                "type": "number"
              },
              "maxItems": 100,
              "minItems": 1,
              "type": "array"
            },
            "probability_queries": {
              "description": "Probabilities to read off the fitted normal model: {\"below\": v}, {\"above\": v} or {\"between\": [a, b]}.",
              "items": {
                "additionalProperties": false,
                "maxProperties": 1,
                "minProperties": 1,
                "properties": {
                  "above": {
                    "type": "number"
                  },
                  "below": {
                    "type": "number"
                  },
                  "between": {
                    "items": {
                      "type": "number"
                    },
                    "maxItems": 2,
                    "minItems": 2,
                    "type": "array"
                  }
                },
                "type": "object"
              },
              "maxItems": 50,
              "type": "array"
            },
            "table": {
              "description": "BigQuery table to read instead of `points`: project.dataset.table, readable by the node's service account (public datasets are). Needs x_column and y_column.",
              "type": "string"
            },
            "x_column": {
              "description": "Numeric column for x, with `table`.",
              "type": "string"
            },
            "y_column": {
              "description": "Numeric column for y, with `table`.",
              "type": "string"
            }
          },
          "required": [],
          "type": "object"
        },
        "bodyType": {
          "enum": [
            "json",
            "form-data",
            "text"
          ],
          "type": "string"
        },
        "method": {
          "enum": [
            "POST",
            "PUT",
            "PATCH"
          ],
          "type": "string"
        },
        "type": {
          "const": "http",
          "type": "string"
        }
      },
      "required": [
        "type",
        "method",
        "bodyType",
        "body"
      ],
      "type": "object"
    },
    "output": {
      "properties": {
        "example": {
          "$schema": "https://json-schema.org/draft/2020-12/schema",
          "description": "The 200 body of every paid /work call. `result` is the worker's own output (its schema is per route); everything else is the same on all 38 routes. A receipt for the job is at `receipt_url`.",
          "properties": {
            "billing_warning": {
              "description": "Present only when the charge was recorded with a caveat.",
              "examples": [
                "settlement pending"
              ],
  

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