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Summary and Prediction Functions

Functions for extracting coefficient statistics and making predictions with confidence intervals.

Summary Functions

Return coefficient statistics in tidy format (like R's broom::tidy).

Available Functions

ps.ols_summary(y, *x, with_intercept=True) -> pl.Expr
ps.ridge_summary(y, *x, lambda_=1.0, with_intercept=True) -> pl.Expr
ps.elastic_net_summary(y, *x, lambda_=1.0, alpha=0.5, with_intercept=True) -> pl.Expr
ps.wls_summary(y, weights, *x, with_intercept=True) -> pl.Expr
ps.rls_summary(y, *x, forgetting_factor=0.99, with_intercept=True) -> pl.Expr
ps.bls_summary(y, *x, lower_bound=None, upper_bound=None, with_intercept=True) -> pl.Expr
ps.logistic_summary(y, *x, with_intercept=True) -> pl.Expr
ps.poisson_summary(y, *x, with_intercept=True) -> pl.Expr
ps.negative_binomial_summary(y, *x, theta=None, with_intercept=True) -> pl.Expr
ps.tweedie_summary(y, *x, var_power=1.5, with_intercept=True) -> pl.Expr
ps.probit_summary(y, *x, with_intercept=True) -> pl.Expr
ps.cloglog_summary(y, *x, with_intercept=True) -> pl.Expr
ps.alm_summary(y, *x, distribution="normal", with_intercept=True) -> pl.Expr

Formula variants also available: ps.ols_formula_summary(formula, ...), etc.

Returns: See Summary Output

Example

# Get coefficient table per group
df.group_by("group").agg(
    ps.ols_summary("y", "x1", "x2").alias("coef")
).explode("coef").unnest("coef")

Output: | group | term | estimate | std_error | statistic | p_value | |-------|------|----------|-----------|-----------|---------| | A | intercept | 1.234 | 0.123 | 10.03 | 0.000 | | A | x1 | 0.567 | 0.045 | 12.60 | 0.000 | | A | x2 | -0.234 | 0.067 | -3.49 | 0.001 |

Prediction Functions

Return per-row predictions with optional confidence/prediction intervals.

Signature

ps.ols_predict(
    y: Union[pl.Expr, str],
    *x: Union[pl.Expr, str],
    add_intercept: bool = True,
    interval: str | None = None,  # None, "confidence", "prediction"
    level: float = 0.95,
    null_policy: str = "drop",    # "drop", "drop_y_zero_x"
) -> pl.Expr

Available Functions

All models have prediction functions: - ols_predict, ridge_predict, elastic_net_predict - wls_predict, rls_predict, bls_predict, nnls_predict - logistic_predict, poisson_predict, negative_binomial_predict - tweedie_predict, probit_predict, cloglog_predict - alm_predict

Formula variants also available: ps.ols_formula_predict(formula, ...), etc.

Returns: See Prediction Output

Parameters

Parameter Description
interval None (point only), "confidence" (mean interval), "prediction" (individual interval)
level Confidence level (default 0.95 for 95% intervals)
null_policy How to handle missing values: "drop" or "drop_y_zero_x"

Example

# Per-group predictions with 95% prediction intervals
df.with_columns(
    ps.ols_predict("y", "x1", "x2", interval="prediction", level=0.95)
        .over("group").alias("pred")
).unnest("pred")

Output: | group | y | x1 | x2 | prediction | lower | upper | |-------|---|----|----|------------|-------|-------| | A | 5.2 | 1.0 | 2.0 | 5.15 | 3.21 | 7.09 | | A | 3.8 | 0.5 | 1.5 | 3.92 | 1.98 | 5.86 |

Interval Types

Type Description Use Case
None Point prediction only Fast prediction
"confidence" Interval for mean response Uncertainty about regression line
"prediction" Interval for individual observation Forecasting new observations

Note: Prediction intervals are always wider than confidence intervals because they account for both uncertainty in the regression line and individual observation variance.

See Also