#! /usr/bin/env python3
#
def homes_model ( ):

#*****************************************************************************80
#
## homes_model() seeks the best linear model for home sale prices.
#
#  Modified:
#
#    31 January 2022
#
  from sklearn.linear_model import LinearRegression
  import matplotlib.pyplot as plt
  import numpy as np

  print ( "home_model:" )
  print ( "  Find best linear model for home sales." )
  print ( "  bill = c0 + c1 * area + c2 * rooms + c3 * beds + c4 * baths" )
  print ( "       + c5 * age + c6 * lot + c7 * tax" )
#
#  Get the data.
#
  filename = 'homes_data.txt'
  data = np.loadtxt ( filename )
  n, d = np.shape ( data )
  print ( "  Data from " + filename + " involves n =", n, "items with dimension d =", d )
#
#  Analyze the data
#
  print ( "  Data statistics:" )
  print ( "    Min      = ", np.min ( data, axis = 0 ) )
  print ( "    Max      = ", np.max ( data, axis = 0 ) )
  print ( "    Range    = ", np.max ( data, axis = 0 ) - np.min ( data, axis = 0 ) )
  print ( "    Mean     = ", np.mean ( data, axis = 0 ) )
  print ( "    Variance = ", np.var ( data, axis = 0 ) )
#
#  Display a histogram of the asking price data, in data[:,0]
#
  plt.clf ( )
  plt.hist ( data[:,0], bins = 15 )
  plt.grid ( True )
  plt.title ( 'Asking price histogram' )
  filename = 'homes_histogram.png'
  plt.savefig ( filename )
  print ( '  Graphics saved as "%s"' % ( filename ) )
  plt.show ( )
  plt.clf ( )
#
#  Set up the linear system X * c = y
#  y = selling = data[1]
#  X = data[2,3,4,5,6,7,8]
#
  X = np.c_ [ np.ones ( n ), data[:,2:9] ]
  y = data[:,0]
#
#  Find c using numpy linalg.lstsq()
#
  c4, _, _, _ = np.linalg.lstsq ( X, y, rcond = None )
  print ( "  C = ", c4 )
  r4 = np.dot ( X, c4 ) - y
  mse4 = np.sum ( r4**2 ) / n
  print ( "  MSE = ", mse4 )
#
#  Make a predictions:
#
  area = 2000
  rooms = 9
  beds = 3
  baths = 2
  age = 50
  lot = 0.45
  taxes = 2500

  y4 = c4[0] + c4[1] * area + c4[2] * rooms + c4[3] * beds + c4[4] * baths\
     + c4[5] * age + c4[6] * lot + c4[7] * taxes

  y_actual = 100000

  print ( "" )
  print ( "  For area = ", area, "rooms = ", rooms, "beds = ", beds )
  print ( "      baths = ", baths, "age = ", age, "lot = ", lot )
  print ( "      taxes = ", taxes )
  print ( "  the model predicts a selling price $", y4 )
  print ( "  The actual selling price was       $", y_actual )

  return

if ( __name__ == "__main__" ):
  homes_model ( )