"""retta di regressione pagine n 19 pag 106 Impedovo"""
from graftarta2 import Graf
from graphics import *
X=[]
for i in range(13):
    X.append(1988+i)
#print X, len(X)
Y=[546,598,660,720,759,782,827,894,951,994,1039,1072,1129]

def media(Lista):
    """ media, varianza dei valori in Lista, sqm
    """
    somma = 0
    sommaqua = 0
    n = len(Lista)
    for k in Lista:
        somma = somma+k
        sommaqua = sommaqua+k*k
    m = float(somma)/n
    varian = float(sommaqua)/n-m*m
    sqm=varian**0.5
    #print 'media ',m, ' varianza ', varian,'  sqm ', sqm
    return m, varian, sqm

def covarianza(X,Y):
    prod=[]
    for i in range(len(X)):
        prod.append(X[i]*Y[i])
    mediaX=media(X)
    mediaY=media(Y)
    mediaXY=media(prod)
    return mediaXY[0]-mediaX[0]*mediaY[0]

medX, varX, sqmX=media(X)
medY, varY, sqmY=media(Y)
cov=covarianza(X,Y)
a=cov/varX
b=medY-a*medX
print a, b
#print m[0]
gr=Graf("retta di regressione",600,400)
gr.coordinate(-2,-100,13,1400,True)
for i in range(len(X)):
    Point(X[i]-1988,Y[i]).draw(gr)
def f(x):
    return a*(x+1988)+b
gr.colorePenna("red")
gr.grafico(f,0,13)