python_for_sport_scientists_pt_3_full.py

import pandas as pd
import seaborn as sns

# Part 1 functions
def mean(arr):
  return sum(arr) / len(arr)

def isEven (arr):
  return arr % 2 == 0

def half (arr):
  if isEven(len(arr)):
    return int(len(arr)/2) - 1
  else:
    return int(len(arr)/2)

def median (arr):
    sortedList = sorted(arr)
    index = half(sortedList)
    if isEven(len(sortedList)):
        return mean([ sortedList[index], sortedList[index + 1] ])
    else:
        return sortedList[index]

# Part 2 functions
def square(x):
    return x * x

def sumOfSquaredDifferences (arr):
    xBar = mean(arr)
    differences = map(lambda x: x - xBar, arr)
    squaredDifferences = map(square, differences)
    return sum(squaredDifferences)

def variance (arr):
    n = len(arr)
    return sumOfSquaredDifferences(arr) / (n-1)

def sqrt (x):
    return x**(1/2)

def stDev (arr):
    return sqrt(variance(arr))

# Part 3 numerator functions
def n (arr):
    return arr.count()

def product (x, y):
    return x * y

def sumXTimesY (x, y):
    return sum(map(product, x, y))

def numerator (x, y):
    return n(x) * sumXTimesY(x, y) - sum(x) * sum(y)

# Part 3 denominator functions

def sumOfSquares (arr):
    return sum(map(square, arr))

def denominator (x, y):
    return sqrt((n(x) * sumOfSquares(x) - square(sum(x))) * (n(y) * sumOfSquares(y) - square(sum(y))))

# Part 3 final function
def r (x, y):
    return numerator(x, y) / denominator(x, y)

# data
data = [
  {"name": "John",  "distance": 5602,  "high-speed-running": 504},
  {"name": "Mike",  "distance": 5242,  "high-speed-running": 622},
  {"name": "Chad",  "distance": 4825,  "high-speed-running": 453},
  {"name": "Phil",  "distance": 611,   "high-speed-running": 500},
  {"name": "Tyler", "distance": 5436,  "high-speed-running": 409}
]

df = pd.DataFrame(data)

weekData = [
  { "name": "John",  "distance": 35.4,  "high-speed-running": 3.65, "week": 1 },
  { "name": "Mike",  "distance": 32.9,  "high-speed-running": 3.77, "week": 1 },
  { "name": "Chad",  "distance": 27.2,  "high-speed-running": 3.02, "week": 1 },
  { "name": "Phil",  "distance": 20.5,  "high-speed-running": 2.01, "week": 1 },
  { "name": "Tyler", "distance": 15.3,  "high-speed-running": 2.09, "week": 1 },
  { "name": "John",  "distance": 38.4,  "high-speed-running": 4.95, "week": 2 },
  { "name": "Mike",  "distance": 37.9,  "high-speed-running": 4.97, "week": 2 },
  { "name": "Chad",  "distance": 33.2,  "high-speed-running": 4.42, "week": 2 },
  { "name": "Phil",  "distance": 25.5,  "high-speed-running": 3.91, "week": 2 },
  { "name": "Tyler", "distance": 19.3,  "high-speed-running": 3.09, "week": 2 },
]

weekDf = pd.DataFrame(data=weekData)

# plots
plot = sns.lmplot(x='high-speed-running', y='distance', data=weekDf)

# operation
r(weekDf['high-speed-running'], weekDf['distance'])
# 0.8803706140091168