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144 lines
3.8 KiB
SQL
144 lines
3.8 KiB
SQL
DROP TABLE IF EXISTS series;
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CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
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/* Тестовые данные */
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INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);
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/* varSamp */
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SELECT varSamp(x_value) FROM (SELECT x_value FROM series LIMIT 0);
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SELECT varSamp(x_value) FROM (SELECT x_value FROM series LIMIT 1);
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SELECT round(abs(res1 - res2), 6) FROM
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(
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SELECT
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varSamp(x_value) AS res1,
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(sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1) AS res2
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FROM series
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);
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/* stddevSamp */
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SELECT stddevSamp(x_value) FROM (SELECT x_value FROM series LIMIT 0);
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SELECT stddevSamp(x_value) FROM (SELECT x_value FROM series LIMIT 1);
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SELECT round(abs(res1 - res2), 6) FROM
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(
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SELECT
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stddevSamp(x_value) AS res1,
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sqrt((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1)) AS res2
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FROM series
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);
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/* varPop */
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SELECT varPop(x_value) FROM (SELECT x_value FROM series LIMIT 0);
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SELECT varPop(x_value) FROM (SELECT x_value FROM series LIMIT 1);
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SELECT round(abs(res1 - res2), 6) FROM
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(
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SELECT
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varPop(x_value) AS res1,
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(sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count() AS res2
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FROM series
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);
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/* stddevPop */
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SELECT stddevPop(x_value) FROM (SELECT x_value FROM series LIMIT 0);
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SELECT stddevPop(x_value) FROM (SELECT x_value FROM series LIMIT 1);
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SELECT round(abs(res1 - res2), 6) FROM
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(
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SELECT
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stddevPop(x_value) AS res1,
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sqrt((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count()) AS res2
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FROM series
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);
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/* covarSamp */
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SELECT covarSamp(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 0);
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SELECT covarSamp(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 1);
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SELECT round(abs(COVAR1 - COVAR2), 6)
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FROM
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(
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SELECT
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arrayJoin([1]) AS ID2,
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covarSamp(x_value, y_value) AS COVAR1
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FROM series
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) ANY INNER JOIN
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(
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SELECT
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arrayJoin([1]) AS ID2,
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sum(VAL) / (count() - 1) AS COVAR2
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FROM
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(
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SELECT (X - AVG_X) * (Y - AVG_Y) AS VAL
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FROM
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(
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SELECT
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toUInt32(arrayJoin([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) AS ID,
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avg(x_value) AS AVG_X,
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avg(y_value) AS AVG_Y
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FROM series
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) ANY INNER JOIN
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(
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SELECT
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i AS ID,
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x_value AS X,
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y_value AS Y
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FROM series
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) USING ID
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)
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) USING ID2;
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/* covarPop */
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SELECT covarPop(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 0);
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SELECT covarPop(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 1);
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SELECT round(abs(COVAR1 - COVAR2), 6)
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FROM
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(
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SELECT
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arrayJoin([1]) AS ID2,
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covarPop(x_value, y_value) AS COVAR1
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FROM series
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) ANY INNER JOIN
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(
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SELECT
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arrayJoin([1]) AS ID2,
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sum(VAL) / count() AS COVAR2
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FROM
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(
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SELECT (X - AVG_X) * (Y - AVG_Y) AS VAL
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FROM
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(
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SELECT
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toUInt32(arrayJoin([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) AS ID,
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avg(x_value) AS AVG_X,
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avg(y_value) AS AVG_Y
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FROM series
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) ANY INNER JOIN
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(
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SELECT
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i AS ID,
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x_value AS X,
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y_value AS Y
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FROM series
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) USING ID
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)
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) USING ID2;
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/* corr */
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SELECT corr(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 0);
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SELECT corr(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 1);
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SELECT round(abs(corr(x_value, y_value) - covarPop(x_value, y_value) / (stddevPop(x_value) * stddevPop(y_value))), 6) FROM series;
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