pts = [(-1,4),(-1,6),(0,4),(2,2),(2,-1),(5,0)]
var('x')
n=len(pts)
xs = []
xsq = []
ys = []
xy = []
ysq = []
for k in range(n):
xtemp = pts[k][0]
ytemp = pts[k][1]
xs.append(xtemp)
ys.append(ytemp)
xsq.append(xtemp^2)
ysq.append(ytemp^2)
xy.append(xtemp*ytemp)
SUMx = sum(xs)
SUMy = sum(ys)
SUMxy = sum(xy)
SUMxsq = sum(xsq)
SUMysq = sum(ysq)
A = matrix([[SUMxsq,SUMx],[SUMx,n]])
show(A)
b = matrix([[SUMxy],[SUMy]])
show(b)
c = A.inverse()*b
m = float(c[0][0])
intercept = float(c[1][0])
T = "$ y = %s"%str(latex(m))+" \cdot x + %s$"%str(latex(intercept))
G = points(pts,size=30,title=T)
f = m*x+intercept
G += plot(f,x,-2,5,color='green')
show(G)
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# This part for graphs to use with MC Math Coach
pts = [(-2,4),(3,1)]
G = points(pts,size=90,color='red')
m = (1-4)/(3+2)
b = 4-m*(-2)
G += plot(m*x+b,(x,-3,5))
show(G)
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# This part for graphs to use with MC Math Coach
m = (1-4)/(3+2)
b = 4-m*(-2)
pts = [(-2,4),(3,1),(1,m+b),(4,4*m+b)]
G = points(pts,size=90,color='red')
G += plot(m*x+b,(x,-3,5))
show(G)
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# This part for graphs to use with MC Math Coach
m = (1-4)/(3+2)
b = 4-m*(-2)
pts = [(-2,4),(3,1),(1,3),(4,1)]
G = points(pts,size=90,color='red')
# G += plot(m*x+b,(x,-3,5))
show(G)
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# This interactive cell allows the user to repeatedly guess parameters for a line that seek to minimize the Total Squared Error
# between the resulting line and the provided data points. This is included in the book text.
var('x')
@interact
def _(Points = input_box([(-2,4),(3,1),(1,3),(4,1)]),
m = slider(-4,4,0.05,1),b = slider(-2,4,0.05,1)):
G = points(Points,size=20)
xpt = []
ypt = []
f = m*x + b
TSE = 0
for k in range(len(Points)):
x0 = Points[k][0]
xpt.append(x0)
y0 = Points[k][1]
ypt.append(y0)
TSE += (f(x=x0) - y0)^2
G += line([(x0,f(x=x0)),(x0,y0)],color='orange')
G += plot(f,x,min(xpt),max(xpt),color='gray')
T = 'Total Squared Error = $%s$'%str(TSE)
G.show(title = T)
Click to the left again to hide and once more to show the dynamic interactive window |
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