Linear Regression

(ns tmath)

(defn sum [list]
  (reduce + list)
)

(defn mean [list]
    (/ (sum list) (count list))
)

(defn prodsum [data]
  (cond
    (empty? data) 0
    :else (+
        (reduce * (first data))
        (prodsum (rest data))
    )
  )
)

(defn expsum [list]
  (sum (map * list list))
)

(defn nexpsum [data position]
    (-
        (*
            (count data)
            (expsum (map position data))
        )
        (Math/pow (sum (map position data)) 2)
    )
)

(defn nprodsum [data]
  (*
    (count data)
    (prodsum data)
  )
)

(defn pearson [data]
  (/
    (-
      (nprodsum data)
      (*
          (sum (map first data))
          (sum (map last data))
      )
    )
    (Math/sqrt
      (*
        (nexpsum data first)
        (nexpsum data last)
      )
    )
  )
)

(defn dev [n mean]
    (Math/pow (- n mean) 2)
)

(defn stddev [list]
    (Math/sqrt
        (*
            (/
                1
                (count list)
            )
            (sum (map dev list (repeat (count list) (mean list))))
        )
    )
)

(defn slope [data]
  (*
    (pearson data)
    (/
      (stddev (map last data))
      (stddev (map first data))
    )
  )
)

(defn yintercept [data]
  (-
    (mean (map last data))
    (* (slope data) (mean (map first data)))
  )
)

(defn lreg [data]
  (str "f(x) = " (slope data) "x + " (yintercept data))
)

(lreg [
[     3.385    44.500]
[     0.480    15.500]
[     1.350     8.100]
[   465.000   423.000]
[    36.330   119.500]
[    27.660   115.000]
[    14.830    98.200]
[     1.040     5.500]
[     4.190    58.000]
[     0.425     6.400]
[     0.101     4.000]
[     0.920     5.700]
[     1.000     6.600]
[     0.005     0.140]
[     0.060     1.000]
[     3.500    10.800]
[     2.000    12.300]
[     1.700     6.300]
[  2547.000  4603.000]
[     0.023     0.300]
[   187.100   419.000]
[   521.000   655.000]
[     0.785     3.500]
[    10.000   115.000]
[     3.300    25.600]
[     0.200     5.000]
[     1.410    17.500]
[   529.000   680.000]
[   207.000   406.000]
[    85.000   325.000]
[     0.750    12.300]
[    62.000  1320.000]
[  6654.000  5712.000]
[     3.500     3.900]
[     6.800   179.000]
[    35.000    56.000]
[     4.050    17.000]
[     0.120     1.000]
[     0.023     0.400]
[     0.010     0.250]
[     1.400    12.500]
[   250.000   490.000]
[     2.500    12.100]
[    55.500   175.000]
[   100.000   157.000]
[    52.160   440.000]
[    10.550   179.500]
[     0.550     2.400]
[    60.000    81.000]
[     3.600    21.000]
[     4.288    39.200]
[     0.280     1.900]
[     0.075     1.200]
[     0.122     3.000]
[     0.048     0.330]
[   192.000   180.000]
[     3.000    25.000]
[   160.000   169.000]
[     0.900     2.600]
[     1.620    11.400]
[     0.104     2.500]
[     4.235    50.400]
])