feat(sql): add regr_rmse, regression t-statistics and interval to_timezone

[aydinmrnv]

Fixes questdb#7400
Fixes questdb#7401
Fixes questdb#7402

This branch bundles three related SQL changes. Each is described in its own section below.

questdb#7401 - regr_rmse and regression t-statistic aggregates

Adds three aggregate functions over (y, x) pairs:

• regr_rmse(y, x) - root mean square error of the simple linear regression, sqrt(SSE / n). It divides by n rather than n - 2, so it is a biased estimator of the error standard deviation but matches the literal "root mean square error" definition.
• regr_slope_tstat(y, x) - t-statistic for the slope under the null hypothesis that the true slope is zero, slope / SE(slope).
• regr_intercept_tstat(y, x) - t-statistic for the intercept under the null hypothesis that the true intercept is zero, intercept / SE(intercept).

All three extend AbstractRegressionGroupByFunction and reuse its six Welford state slots, so they inherit parallel group-by support through the existing Chan pairwise merge with no new merge code.

Edge cases: the t-statistics have n - 2 degrees of freedom and return NULL for fewer than three points. A non-varying X (Sxx = 0) returns NULL, matching regr_slope/regr_r2. A perfect fit (SSE <= 0) returns NULL for the t-statistics rather than +/-Infinity; regr_rmse clamps tiny negative rounding results to zero so sqrt does not produce NaN.

questdb#7400 - to_timezone() for interval values

Adds a to_timezone(INTERVAL, tz) overload alongside the existing timestamp overload. It shifts both endpoints of the interval by each endpoint's own zone offset, so an interval that straddles a DST transition is converted with the correct offset on each side rather than a single shared offset. Constant, runtime-constant and non-constant timezone arguments are handled on separate paths, mirroring the timestamp overload. A null endpoint yields Interval.NULL; a null timezone is rejected at compile time; an unparseable timezone in a per-row argument leaves the interval unchanged.

questdb#7402 - point unclosed-parenthesis errors at the parenthesis, not at FROM

When a projection list ends at FROM while a ( is still open (for example a function call whose ) was forgotten), the parser previously reported the error at FROM, which is only where it first noticed the imbalance. The parser now looks ahead over the rest of the statement: if no ) closes the enclosing paren before the statement ends, it points the error at the offending ( instead. A stray from inside a balanced pair is a different problem and still reports dangling literal at from.

Tradeoffs and notes

• The unclosed-paren fix adds a bounded look-ahead over the remaining tokens on the error path only; it does not affect successful parses.
• regr_rmse intentionally normalises by n, not n - 2; consumers wanting the residual standard error should not use it as a drop-in.
• No documentation pages are included in this branch.

Test plan

• New RegressionRmseFunctionFactoryTest, RegressionSlopeTStatFunctionFactoryTest, RegressionInterceptTStatFunctionFactoryTest - values against hand-computed expectations, NULL handling for n < 3, constant/non-varying X, and perfect-fit cases.
• New ToTimezoneIntervalFunctionFactoryTest (parameterized over MICRO and NANO timestamps) - area names, DST straddle, fixed offsets, null interval, null and invalid timezones, constant and bind-variable timezones.
• New SqlParserTest#testUnclosedParenthesisIssue6010 - unclosed paren points at (, stray from still reports dangling literal.
• Regression: full SqlParserTest (1084 tests), existing ToTimezoneTimestampFunctionFactoryTest, RegressionSlopeFunctionFactoryTest and RegressionInterceptFunctionFactoryTest all pass unchanged.

🤖 Generated with Claude Code

https://claude.ai/code/session_013n4FXQQSBadC9pw9Sdzg8b

---

Generated by Claude Code

[coderabbitai]

Important

Review skipped

Auto reviews are disabled on this repository. Please check the settings in the CodeRabbit UI or the .coderabbit.yaml file in this repository. To trigger a single review, invoke the @coderabbitai review command.

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Pro Plus

Run ID: 10009623-f43d-43b8-8f39-eff3b8778a1e

You can disable this status message by setting the reviews.review_status to false in the CodeRabbit configuration file.

Use the checkbox below for a quick retry:

• 🔍 Trigger review

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch claude/questdb-assigned-tasks-rf2z26

---

_{Comment @coderabbitai help to get the list of available commands.}