Problem

Am looking to apply the y = mx + b equation (where m is SLOPE, b is INTERCEPT) to a data set, which is retrieved as shown in the SQL code. The values from the (MySQL) query are:

SLOPE = 0.0276653965651912
INTERCEPT = -57.2338357550468

SQL 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 ) ) < 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 <> 'M'
  GROUP BY Y.YEAR
  ORDER BY Y.YEAR
) t

Data

The data is visualized here:

Question

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)?

(1900 * 0.0276653965651912) + (-57.2338357550468) = -4.66958228

(2009 * 0.0276653965651912) + (-57.2338357550468) = -1.65405406

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).

Related Sites

• Least absolute deviations
• Robust regression

Thank you!