基本統計学 3.2 線形回帰 例3.2

test.hs

import Data.List

data RegressionCalcTable = RegressionCalcTable {
      sumX    :: Double,
      sumY    :: Double,
      sumXX   :: Double,
      sumXY   :: Double,
      sumYY   :: Double,
      elemNum :: Double
} deriving (Show, Eq)

-- table 3.2
height :: [Double]
height = [171,180,169,173,173,
          163,168,176,173,174,
          164,171,172,172,175,
          163,163,162,167,170,
          173,170,170,175,170]

weight :: [Double]
weight = [62,71,53,78,59,
          54,62,60,60,62,
          50,66,69,63,62,
          65,53,52,60,67,
          70,67,56,68,56]

average :: [Double] -> Double
average [] = 0
average xs = (sum xs) / fromIntegral (length xs)

calcTable :: [Double] -> [Double] -> RegressionCalcTable
calcTable xs ys = RegressionCalcTable {
  sumX    = sum xs,
  sumY    = sum ys,
  sumXX   = foldr (\x acc     -> acc + x * x) 0 xs,
  sumXY   = foldr (\(x,y) acc -> acc + x * y) 0 $ zip xs ys,
  sumYY   = foldr (\y acc     -> acc + y * y) 0 ys,
  elemNum = fromIntegral $ length xs
}

normalEquation :: RegressionCalcTable -> (Double, Double)
normalEquation (RegressionCalcTable sx sy sxx sxy syy n) = (a, b) 
  where
    a = (sxx * sy - sx * sxy) / (n * sxx - sx * sx)
    b = (n * sxy - sx * sy)   / (n * sxx - sx * sx)

linearRegression :: [Double] -> [Double] -> (Double -> Double)
linearRegression xs ys = (\x -> a + b * x)
  where
    (a, b) = normalEquation $ calcTable xs ys

実行例
*Main> let f = linearRegression height weight
*Main> f 172
63.33125591669297

身長172cmはだいたい63.3kg