these_calculations_are_not_very_kind.hs

-- Linear correlation stuff for MATH 211, yay?

-- An error, but a bit more condescending than usual.
(ಠ_ಠ) x = error ("ಠ_ಠ "++x++" ಠ_ಠ")

ccoeff :: [Double] -> [Double] -> Double
ccoeff xs ys = (n*xyΣ - xΣ*yΣ)/((n*x²Σ - xΣ**2.0)*(n*y²Σ-yΣ**2.0))**0.5
   where xΣ  = sum xs
         yΣ  = sum ys
         xyΣ = sum $ zipWith (*) xs ys
         x²Σ = sum $ map (^2) xs
         y²Σ = sum $ map (^2) ys
         n   = if (length xs == length ys)
                 then fromIntegral (length xs) :: Double
               else ಠ_ಠ "Lists not the same size"
         β₁  = (n*xyΣ-xΣ*yΣ)/(n*x²Σ-xΣ**2)
         β₀  = yΣ/n - β₁*(xΣ/n)

linreg :: [Double] -> [Double] -> (Double,Double)
linreg xs ys = (β₁,β₀)
   where xΣ  = sum xs
         yΣ  = sum ys
         xyΣ = sum $ zipWith (*) xs ys
         x²Σ = sum $ map (^2) xs
         y²Σ = sum $ map (^2) ys
         n   = if (length xs == length ys)
                 then fromIntegral (length xs) :: Double
               else ಠ_ಠ "Lists not the same size"
         β₁  = (n*xyΣ-xΣ*yΣ)/(n*x²Σ-xΣ**2)
         β₀  = yΣ/n - β₁*(xΣ/n)

linreg' :: [Double] -> [Double] -> (Double -> Double)
-- ^ Return a function for the linear regression line
-- of the data set. 
linreg' xs ys = \x -> β₁*x + β₀
    where (β₁,β₀) = linreg xs ys

stdErr :: [Double] -> [Double] -> Double
stdErr xs ys = ((y²Σ-β₀*yΣ-β₁*xyΣ)/(n-2))**0.5
   where xΣ  = sum xs
         yΣ  = sum ys
         xyΣ = sum $ zipWith (*) xs ys
         x²Σ = sum $ map (^2) xs
         y²Σ = sum $ map (^2) ys
         n   = if (length xs == length ys)
                 then fromIntegral (length xs) :: Double
               else ಠ_ಠ "Lists not the same size"
         β₁  = (n*xyΣ-xΣ*yΣ)/(n*x²Σ-xΣ**2)
         β₀  = yΣ/n - β₁*(xΣ/n)