#!/usr/bin/env python
# coding: utf-8

# In[2]:


# HIDDEN
from datascience import *
get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
import numpy as np


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# HIDDEN

def standard_units(any_numbers):
    "Convert any array of numbers to standard units."
    return (any_numbers - np.mean(any_numbers))/np.std(any_numbers)  

def correlation(t, x, y):
    return np.mean(standard_units(t.column(x))*standard_units(t.column(y)))

def slope(table, x, y):
    r = correlation(table, x, y)
    return r * np.std(table.column(y))/np.std(table.column(x))

def intercept(table, x, y):
    a = slope(table, x, y)
    return np.mean(table.column(y)) - a * np.mean(table.column(x))


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galton = Table.read_table('galton.csv')


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galton


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correlation(galton, 'father', 'mother')


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def galton_multiple_mse(a, b, c):
    y = galton.column('childHeight')
    fitted = a*galton.column('father') + b*galton.column('mother') + c
    return np.mean((y - fitted) ** 2)


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best_quad = minimize(galton_multiple_mse)


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best_quad


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correlation(galton, 'father', 'childHeight')


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correlation(galton, 'mother', 'childHeight')


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best_quad


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intercept(galton, 'midparentHeight', 'childHeight')


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slope(galton, 'midparentHeight', 'childHeight')


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best_quad.item(0) + best_quad.item(1)


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best_quad.item(0) + best_quad.item(1)/1.08


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