diff --git a/mealy.cabal b/mealy.cabal
--- a/mealy.cabal
+++ b/mealy.cabal
@@ -1,6 +1,6 @@
 cabal-version: 2.4
 name:          mealy
-version:       0.3.0
+version:       0.4.0
 license:       BSD-3-Clause
 copyright:     Tony Day (c) 2013 - 2022
 maintainer:    tonyday567@gmail.com
@@ -21,7 +21,7 @@
 
 category:      folding
 build-type:    Simple
-tested-with:   GHC ==8.8.4 || ==8.10.7 || ==9.2.1
+tested-with:   GHC ==8.8.4 || ==8.10.7 || ==9.2.4 || ==9.4.2
 
 source-repository head
   type:     git
@@ -46,10 +46,11 @@
     , containers         ^>=0.6.2
     , mwc-probability    ^>=2.3.1
     , numhask            ^>=0.10
+    , numhask-array      ^>=0.10.1
     , optics-core        ^>=0.4
     , primitive          ^>=0.7.2
     , profunctors        ^>=5.6.2
     , tdigest            ^>=0.2.1
-    , text               ^>=1.2.4
+    , text               >=1.2.4 && < 2.1
     , vector             ^>=0.12.3
     , vector-algorithms  ^>=0.8.0
diff --git a/src/Data/Mealy.hs b/src/Data/Mealy.hs
--- a/src/Data/Mealy.hs
+++ b/src/Data/Mealy.hs
@@ -1,5 +1,6 @@
 {-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE DerivingVia #-}
 {-# LANGUAGE DuplicateRecordFields #-}
 {-# LANGUAGE FlexibleContexts #-}
@@ -46,29 +47,35 @@
     beta1,
     alpha1,
     reg1,
+    beta,
+    alpha,
+    reg,
     asum,
     aconst,
     last,
     maybeLast,
     delay1,
     delay,
+    window,
 
     -- * median
     Medianer (..),
     onlineL1,
     maL1,
-    window,
   )
 where
 
 import Control.Category
 import Control.Exception
+import Data.Functor.Rep
 import Data.List (scanl')
 import Data.Profunctor
 import Data.Sequence (Seq)
 import qualified Data.Sequence as Seq
 import Data.Text (Text)
 import Data.Typeable (Typeable)
+import GHC.TypeLits
+import NumHask.Array as F
 import NumHask.Prelude hiding (L1, asum, fold, id, last, (.))
 
 -- $setup
@@ -117,7 +124,7 @@
 --
 -- __inject__ kicks off state on the initial element of the Foldable, but is otherwise be independent of __step__.
 --
--- > scan (M e s i) (x : xs) = e <$> scanl' s (i x) xs
+-- > scan (M i s e) (x : xs) = e <$> scanl' s (i x) xs
 data Mealy a b = forall c. Mealy (a -> c) (c -> a -> c) (c -> b)
 
 -- | Strict Pair
@@ -373,6 +380,74 @@
 reg1 :: (ExpField a) => Mealy a a -> Mealy (a, a) (a, a)
 reg1 m = (,) <$> alpha1 m <*> beta1 m
 
+data RegressionState (n :: Nat) a = RegressionState
+  { _xx :: F.Array '[n, n] a,
+    _x :: F.Array '[n] a,
+    _xy :: F.Array '[n] a,
+    _y :: a
+  }
+  deriving (Functor)
+
+-- | multiple regression
+--
+-- \[
+-- \begin{align}
+-- {\hat  {{\mathbf  {B}}}}=({\mathbf  {X}}^{{{\rm {T}}}}{\mathbf  {X}})^{{ -1}}{\mathbf  {X}}^{{{\rm {T}}}}{\mathbf  {Y}}
+-- \end{align}
+-- \]
+--
+-- \[
+-- \begin{align}
+-- {\mathbf  {X}}={\begin{bmatrix}{\mathbf  {x}}_{1}^{{{\rm {T}}}}\\{\mathbf  {x}}_{2}^{{{\rm {T}}}}\\\vdots \\{\mathbf  {x}}_{n}^{{{\rm {T}}}}\end{bmatrix}}={\begin{bmatrix}x_{{1,1}}&\cdots &x_{{1,k}}\\x_{{2,1}}&\cdots &x_{{2,k}}\\\vdots &\ddots &\vdots \\x_{{n,1}}&\cdots &x_{{n,k}}\end{bmatrix}}
+-- \end{align}
+-- \]
+--
+-- > let ys = zipWith3 (\x y z -> 0.1 * x + 0.5 * y + 1 * z) xs0 xs1 xs2
+-- > let zs = zip (zipWith (\x y -> fromList [x,y] :: F.Array '[2] Double) xs1 xs2) ys
+-- > fold (beta 0.99) zs
+-- [0.4982692361226971, 1.038192474255091]
+beta :: (ExpField a, KnownNat n, Eq a) => a -> Mealy (F.Array '[n] a, a) (F.Array '[n] a)
+beta r = M inject step extract
+  where
+    -- extract :: Averager (RegressionState n a) a -> (F.Array '[n] a)
+    extract (A (RegressionState xx x xy y) c) =
+      (\a b -> recip a `F.mult` b)
+        ((one / c) .* (xx - F.expand (*) x x))
+        ((xy - (y .* x)) *. (one / c))
+    step x (xs, y) = rsOnline r x (inject (xs, y))
+    -- inject :: (F.Array '[n] a, a) -> Averager (RegressionState n a) a
+    inject (xs, y) =
+      A (RegressionState (F.expand (*) xs xs) xs (y .* xs) y) one
+{-# INLINEABLE beta #-}
+
+rsOnline :: (Field a, KnownNat n) => a -> Averager (RegressionState n a) a -> Averager (RegressionState n a) a -> Averager (RegressionState n a) a
+rsOnline r (A (RegressionState xx x xy y) c) (A (RegressionState xx' x' xy' y') c') =
+  A (RegressionState (liftR2 d xx xx') (liftR2 d x x') (liftR2 d xy xy') (d y y')) (d c c')
+  where
+    d s s' = r * s + s'
+
+-- | alpha in a multiple regression
+alpha :: (ExpField a, KnownNat n, Eq a) => a -> Mealy (F.Array '[n] a, a) a
+alpha r = (\xs b y -> y - sum (liftR2 (*) b xs)) <$> lmap fst (arrayify $ ma r) <*> beta r <*> lmap snd (ma r)
+{-# INLINEABLE alpha #-}
+
+arrayify :: (HasShape s) => Mealy a b -> Mealy (F.Array s a) (F.Array s b)
+arrayify (M sExtract sStep sInject) = M extract step inject
+  where
+    extract = fmap sExtract
+    step = liftR2 sStep
+    inject = fmap sInject
+
+-- | multiple regression
+--
+-- > let ys = zipWith3 (\x y z -> 0.1 * x + 0.5 * y + 1 * z) xs0 xs1 xs2
+-- > let zs = zip (zipWith (\x y -> fromList [x,y] :: F.Array '[2] Double) xs1 xs2) ys
+-- > fold (reg 0.99) zs
+-- ([0.4982692361226971, 1.038192474255091],2.087160803386695e-3)
+reg :: (ExpField a, KnownNat n, Eq a) => a -> Mealy (F.Array '[n] a, a) (F.Array '[n] a, a)
+reg r = (,) <$> beta r <*> alpha r
+{-# INLINEABLE reg #-}
+
 -- | accumulated sum
 asum :: (Additive a) => Mealy a a
 asum = M id (+) id
@@ -421,6 +496,11 @@
     step Seq.Empty _ = throw (MealyError "empty seq")
     step (_ Seq.:<| xs) a = xs Seq.|> a
 
+-- | a moving window of a's, most recent at the front of the sequence
+window :: Int -> Mealy a (Seq.Seq a)
+window n = M Seq.singleton (\xs x -> Seq.take n (x Seq.<| xs)) id
+{-# INLINEABLE window #-}
+
 -- | A rough Median.
 -- The average absolute value of the stat is used to callibrate estimate drift towards the median
 data Medianer a b = Medianer
@@ -458,8 +538,3 @@
 maL1 :: (Ord a, Field a, Signed a) => a -> a -> a -> Mealy a a
 maL1 i d r = onlineL1 i d id (* r)
 {-# INLINEABLE maL1 #-}
-
--- | a window of a's
-window :: Int -> Mealy a [a]
-window n = M Seq.singleton (\xs x -> Seq.take n (x Seq.<| xs)) (reverse . toList)
-{-# INLINEABLE window #-}