removedOutput schema / properties / result / properties
Removed value: -{
- "alpha": {
- "description": "Significance level used.",
- "examples": [
- 0.05
- ],
- "type": "number"
- },
- "confidence_level": {
- "description": "1 - alpha: the level of every interval.",
- "examples": [
- 0.95
- ],
- "type": "number"
- },
- "linear_regression": {
- "description": "Ordinary least squares fit of y on x; null when not requested.",
- "properties": {
- "adjusted_r_squared": {
- "description": "R^2 adjusted for degrees of freedom.",
- "examples": [
- 0.995
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "degrees_of_freedom": {
- "description": "n - 2.",
- "examples": [
- 3
- ],
- "type": "integer"
- },
- "f_statistic": {
- "description": "F statistic of the regression (t^2); null when undefined.",
- "examples": [
- 773
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "intercept": {
- "description": "OLS intercept.",
- "examples": [
- 0.08
- ],
- "type": "number"
- },
- "intercept_ci": {
- "description": "Lower and upper bound at the confidence level.",
- "examples": [
- [
- 1.43,
- 2.53
- ]
- ],
- "items": {
- "description": "Bound.",
- "examples": [
- 0
- ],
- "type": "number"
- },
- "type": "array"
- },
- "intercept_std_error": {
- "description": "Standard error of the intercept.",
- "examples": [
- 0.236
- ],
- "type": "number"
- },
- "intercept_t": {
- "description": "t statistic of the intercept; null when undefined.",
- "examples": [
- 0.34
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "r": {
- "description": "Pearson correlation; null when y is constant.",
- "examples": [
- 0.998
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "r_squared": {
- "description": "Coefficient of determination; null when y is constant.",
- "examples": [
- 0.996
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "residual_std_error": {
- "description": "Standard error of the residuals, sqrt(SSE / df).",
- "examples": [
- 0.225
- ],
- "type": "number"
- },
- "slope": {
- "description": "OLS slope.",
- "examples": [
- 1.98
- ],
- "type": "number"
- },
- "slope_ci": {
- "description": "Lower and upper bound at the confidence level.",
- "examples": [
- [
- 1.43,
- 2.53
- ]
- ],
- "items": {
- "description": "Bound.",
- "examples": [
- 0
- ],
- "type": "number"
- },
- "type": "array"
- },
- "slope_std_error": {
- "description": "Standard error of the slope.",
- "examples": [
- 0.071
- ],
- "type": "number"
- },
- "slope_t": {
- "description": "t statistic of the slope; null when undefined.",
- "examples": [
- 27.8
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "sse": {
- "description": "Sum of squared residuals.",
- "examples": [
- 0.152
- ],
- "type": "number"
- },
- "sst": {
- "description": "Total sum of squares of y.",
- "examples": [
- 39.4
- ],
- "type": "number"
- },
- "t_critical": {
- "description": "Two-sided t critical value at alpha with df degrees of freedom.",
- "examples": [
- 3.18
- ],
- "type": "number"
- },
- "x_mean": {
- "description": "Mean of x.",
- "examples": [
- 3
- ],
- "type": "number"
- },
- "y_mean": {
- "description": "Mean of y.",
- "examples": [
- 6.02
- ],
- "type": "number"
- }
- },
- "required": [
- "slope",
- "intercept",
- "r",
- "r_squared",
- "adjusted_r_squared",
- "slope_std_error",
- "intercept_std_error",
- "residual_std_error",
- "degrees_of_freedom",
- "slope_t",
- "intercept_t",
- "t_critical",
- "slope_ci",
- "intercept_ci",
- "f_statistic",
- "sse",
- "sst",
- "x_mean",
- "y_mean"
- ],
- "type": [
- "object",
- "null"
- ]
- },
- "method": {
- "description": "How the numbers were produced.",
- "examples": [
- "Ordinary least squares (closed form). Student t p-values from the regularised incomplete beta function..."
- ],
- "type": "string"
- },
- "metrics": {
- "description": "Metrics computed, in canonical order.",
- "examples": [
- [
- "linear_regression",
- "normal_distribution",
- "p_values",
- "prediction"
- ]
- ],
- "items": {
- "description": "Metric name.",
- "enum": [
- "linear_regression",
- "normal_distribution",
- "p_values",
- "prediction"
- ],
- "examples": [
- "linear_regression"
- ],
- "type": "string"
- },
- "type": "array"
- },
- "n": {
- "description": "Number of points.",
- "examples": [
- 5
- ],
- "type": "integer"
- },
- "normal_distribution": {
- "description": "Normal model of the chosen values; null when not requested.",
- "properties": {
- "excess_kurtosis": {
- "description": "Excess kurtosis; null when the values are constant.",
- "examples": [
- -1.3
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "max": {
- "description": "Largest value.",
- "examples": [
- 10.1
- ],
- "type": "number"
- },
- "mean": {
- "description": "Sample mean.",
- "examples": [
- 6.02
- ],
- "type": "number"
- },
- "median": {
- "description": "Median of the values.",
- "examples": [
- 6.2
- ],
- "type": "number"
- },
- "min": {
- "description": "Smallest value.",
- "examples": [
- 2.1
- ],
- "type": "number"
- },
- "normality": {
- "description": "Jarque-Bera normality test; null when the values are constant.",
- "properties": {
- "null_hypothesis": {
- "description": "What the test rejects.",
- "examples": [
- "the values are normally distributed"
- ],
- "type": "string"
- },
- "p_value": {
- "description": "Chi-square(2) p-value, exp(-JB/2).",
- "examples": [
- 0.81
- ],
- "type": "number"
- },
- "reject_at_alpha": {
- "description": "p_value < alpha: not normal at this alpha.",
- "examples": [
- false
- ],
- "type": "boolean"
- },
- "statistic": {
- "description": "Jarque-Bera statistic.",
- "examples": [
- 0.42
- ],
- "type": "number"
- },
- "test": {
- "const": "jarque_bera",
- "description": "The test.",
- "type": "string"
- }
- },
- "required": [
- "test",
- "statistic",
- "p_value",
- "null_hypothesis",
- "reject_at_alpha"
- ],
- "type": [
- "object",
- "null"
- ]
- },
- "of": {
- "description": "Which values the model fits.",
- "enum": [
- "y",
- "x",
- "residuals"
- ],
- "examples": [
- "y"
- ],
- "type": "string"
- },
- "probabilities": {
- "description": "Answers to probability_queries, in order.",
- "examples": [
- [
- {
- "probability": 0.736,
- "query": {
- "below": 8
- }
- }
- ]
- ],
- "items": {
- "properties": {
- "probability": {
- "description": "Probability under the fitted normal.",
- "examples": [
- 0.736
- ],
- "type": "number"
- },
- "query": {
- "description": "The query as sent.",
- "examples": [
- {
- "below": 8
- }
- ],
- "type": [
- "object"
- ]
- }
- },
- "required": [
- "query",
- "probability"
- ],
- "type": "object"
- },
- "type": "array"
- },
- "quantiles": {
- "description": "Quantiles of the fitted normal; null when degenerate.",
- "items": {
- "properties": {
- "p": {
- "description": "Probability.",
- "examples": [
- 0.95
- ],
- "type": "number"
- },
- "value": {
- "description": "Value at that quantile.",
- "examples": [
- 11.19
- ],
- "type": "number"
- }
- },
- "required": [
- "p",
- "value"
- ],
- "type": "object"
- },
- "type": [
- "array",
- "null"
- ]
- },
- "skewness": {
- "description": "Sample skewness; null when the values are constant.",
- "examples": [
- 0.05
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "std_dev": {
- "description": "Sample standard deviation (n - 1).",
- "examples": [
- 3.14
- ],
- "type": "number"
- },
- "variance": {
- "description": "Sample variance (n - 1).",
- "examples": [
- 9.86
- ],
- "type": "number"
- }
- },
- "required": [
- "of",
- "mean",
- "std_dev",
- "variance",
- "min",
- "max",
- "median",
- "skewness",
- "excess_kurtosis",
- "quantiles",
- "probabilities",
- "normality"
- ],
- "type": [
- "object",
- "null"
- ]
- },
- "notes": {
- "description": "Caveats about the input; empty when there are none.",
- "examples": [
- []
- ],
- "items": {
- "description": "A caveat about a degenerate input.",
- "examples": [
- "The points lie exactly on a line."
- ],
- "type": "string"
- },
- "type": "array"
- },
- "p_values": {
- "description": "Hypothesis tests validated at alpha; null when not requested.",
- "properties": {
- "intercept": {
- "description": "One two-sided Student t test.",
- "properties": {
- "null_hypothesis": {
- "description": "What the test rejects.",
- "examples": [
- "slope = 0 (no linear relationship)"
- ],
- "type": "string"
- },
- "p_value": {
- "description": "Two-sided p-value; null when undefined.",
- "examples": [
- 0.0015
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "significant_at_alpha": {
- "description": "p_value < alpha.",
- "examples": [
- true
- ],
- "type": [
- "boolean",
- "null"
- ]
- },
- "t": {
- "description": "Student t statistic; null when undefined (a perfect fit).",
- "examples": [
- 11.4
- ],
- "type": [
- "number",
- "null"
- ]
- }
- },
- "required": [
- "null_hypothesis",
- "t",
- "p_value",
- "significant_at_alpha"
- ],
- "type": "object"
- },
- "normality_of_residuals": {
- "description": "Jarque-Bera normality test; null when the values are constant.",
- "properties": {
- "null_hypothesis": {
- "description": "What the test rejects.",
- "examples": [
- "the values are normally distributed"
- ],
- "type": "string"
- },
- "p_value": {
- "description": "Chi-square(2) p-value, exp(-JB/2).",
- "examples": [
- 0.81
- ],
- "type": "number"
- },
- "reject_at_alpha": {
- "description": "p_value < alpha: not normal at this alpha.",
- "examples": [
- false
- ],
- "type": "boolean"
- },
- "statistic": {
- "description": "Jarque-Bera statistic.",
- "examples": [
- 0.42
- ],
- "type": "number"
- },
- "test": {
- "const": "jarque_bera",
- "description": "The test.",
- "type": "string"
- }
- },
- "required": [
- "test",
- "statistic",
- "p_value",
- "null_hypothesis",
- "reject_at_alpha"
- ],
- "type": [
- "object",
- "null"
- ]
- },
- "slope": {
- "description": "One two-sided Student t test.",
- "properties": {
- "null_hypothesis": {
- "description": "What the test rejects.",
- "examples": [
- "slope = 0 (no linear relationship)"
- ],
- "type": "string"
- },
- "p_value": {
- "description": "Two-sided p-value; null when undefined.",
- "examples": [
- 0.0015
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "significant_at_alpha": {
- "description": "p_value < alpha.",
- "examples": [
- true
- ],
- "type": [
- "boolean",
- "null"
- ]
- },
- "t": {
- "description": "Student t statistic; null when undefined (a perfect fit).",
- "examples": [
- 11.4
- ],
- "type": [
- "number",
- "null"
- ]
- }
- },
- "required": [
- "null_hypothesis",
- "t",
- "p_value",
- "significant_at_alpha"
- ],
- "type": "object"
- }
- },
- "required": [
- "slope",
- "intercept",
- "normality_of_residuals"
- ],
- "type": [
- "object",
- "null"
- ]
- },
- "prediction": {
- "description": "One entry per predict_x; null when not requested.",
- "items": {
- "properties": {
- "mean_ci": {
- "description": "Lower and upper bound at the confidence level.",
- "examples": [
- [
- 1.43,
- 2.53
- ]
- ],
- "items": {
- "description": "Bound.",
- "examples": [
- 0
- ],
- "type": "number"
- },
- "type": "array"
- },
- "prediction_interval": {
- "description": "Lower and upper bound at the confidence level.",
- "examples": [
- [
- 1.43,
- 2.53
- ]
- ],
- "items": {
- "description": "Bound.",
- "examples": [
- 0
- ],
- "type": "number"
- },
- "type": "array"
- },
- "x": {
- "description": "The x asked for.",
- "examples": [
- 6
- ],
- "type": "number"
- },
- "y_hat": {
- "description": "Predicted y.",
- "examples": [
- 11.96
- ],
- "type": "number"
- }
- },
- "required": [
- "x",
- "y_hat",
- "mean_ci",
- "prediction_interval"
- ],
- "type": "object"
- },
- "type": [
- "array",
- "null"
- ]
- },
- "source": {
- "description": "Where the data came from and how much of it was used.",
- "properties": {
- "gib_processed": {
- "description": "Gibibytes BigQuery scanned; null for inline points.",
- "examples": [
- null
- ],
- "type": [
- "number",
- "null"
- ]
- },
- "rows_available": {
- "description": "Rows with finite x and y in the table; null for inline points.",
- "examples": [
- null
- ],
- "type": [
- "integer",
- "null"
- ]
- },
- "rows_used": {
- "description": "Points the statistics were computed from.",
- "examples": [
- 5
- ],
- "type": "integer"
- },
- "sampled": {
- "description": "True when the table had more usable rows than were read.",
- "examples": [
- false
- ],
- "type": "boolean"
- },
- "sql": {
- "description": "The read-only SQL that ran, when source is bigquery.",
- "examples": [
- null
- ],
- "type": [
- "string",
- "null"
- ]
- },
- "table": {
- "description": "BigQuery table read, when source is bigquery.",
- "examples": [
- null
- ],
- "type": [
- "string",
- "null"
- ]
- },
- "type": {
- "description": "Where the points came from.",
- "enum": [
- "points",
- "bigquery"
- ],
- "examples": [
- "points"
- ],
- "type": "string"
- },
- "x_column": {
- "description": "Column used for x, when source is bigquery.",
- "examples": [
- null
- ],
- "type": [
- "string",
- "null"
- ]
- },
- "y_column": {
- "description": "Column used for y, when source is bigquery.",
- "examples": [
- null
- ],
- "type": [
- "string",
- "null"
- ]
- }
- },
- "required": [
- "type",
- "table",
- "x_column",
- "y_column",
- "sql",
- "rows_available",
- "rows_used",
- "sampled",
- "gib_processed"
- ],
- "type": "object"
- }
-}