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POOptimal two variable linear regression calculation
 

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    <p><strong>Problem</strong></p> <p>Am looking to apply the <code>y = mx + b</code> equation (where m is <code>SLOPE</code>, b is <code>INTERCEPT</code>) to a data set, which is retrieved as shown in the SQL code. The values from the (MySQL) query are:</p> <pre><code>SLOPE = 0.0276653965651912 INTERCEPT = -57.2338357550468 </code></pre> <p><strong>SQL Code</strong></p> <pre><code>SELECT ((sum(t.YEAR) * sum(t.AMOUNT)) - (count(1) * sum(t.YEAR * t.AMOUNT))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as SLOPE, ((sum( t.YEAR ) * sum( t.YEAR * t.AMOUNT )) - (sum( t.AMOUNT ) * sum(power(t.YEAR, 2)))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as INTERCEPT, FROM (SELECT D.AMOUNT, Y.YEAR FROM CITY C, STATION S, YEAR_REF Y, MONTH_REF M, DAILY D WHERE -- For a specific city ... -- C.ID = 8590 AND -- Find all the stations within a 15 unit radius ... -- SQRT( POW( C.LATITUDE - S.LATITUDE, 2 ) + POW( C.LONGITUDE - S.LONGITUDE, 2 ) ) &lt; 15 AND -- Gather all known years for that station ... -- S.STATION_DISTRICT_ID = Y.STATION_DISTRICT_ID AND -- The data before 1900 is shaky; insufficient after 2009. -- Y.YEAR BETWEEN 1900 AND 2009 AND -- Filtered by all known months ... -- M.YEAR_REF_ID = Y.ID AND -- Whittled down by category ... -- M.CATEGORY_ID = '001' AND -- Into the valid daily climate data. -- M.ID = D.MONTH_REF_ID AND D.DAILY_FLAG_ID &lt;&gt; 'M' GROUP BY Y.YEAR ORDER BY Y.YEAR ) t </code></pre> <p><strong>Question</strong></p> <p>The following results (to calculate the start and end points of the line) appear incorrect. Why are the results off by ~10 degrees (e.g., outliers skewing the data)?</p> <blockquote> <p>(1900 * 0.0276653965651912) + (-57.2338357550468) = -4.66958228</p> <p>(2009 * 0.0276653965651912) + (-57.2338357550468) = -1.65405406</p> </blockquote> <p>(Note that the data no longer match the image; the code.)</p> <p>I would have expected the 1900 result to be around 10 (not -4.67) and the 2009 result to be around 11.50 (not -1.65).</p> <p><strong>Related Sites</strong></p> <ul> <li><a href="http://en.wikipedia.org/wiki/Least_absolute_deviations" rel="nofollow noreferrer">Least absolute deviations</a></li> <li><a href="http://en.wikipedia.org/wiki/Robust_regression" rel="nofollow noreferrer">Robust regression</a></li> </ul>
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