Приложение а
import math
T = [300, 400, 500, 600, 700, 800, 900, 1000]
x = [64.18, 79.91, 94.64, 107.53, 118.70, 128.37, 136.82, 144.18]
numbers = 8
s1 = 0
s2 = 0
s3 = 0
s4 = 0
s5 = 0
s6 = 0
s7 = 0
s8 =0
sxy = 0
sx = 0
sy = 0
sx2 = 0
sy2 = 0
n = 8
for i in range(8):
s1 += T[i]
s2 += T[i]**2
s3 += T[i]**3
s4 += T[i]**4
s5 += x[i]
s6 += (x[i] * T[i])
s7 += (T[i]**2 * x[i])
s8 = s8 + T[i]**2
sxy=(sxy+T[i]*x[i])
sy=(sy+x[i])
sx=(sx+T[i])
sx2=(sx2+(T[i])**2)
sy2=(sy2+(x[i])**2
z = n*s2*s4 + s1*s3*s2 + s2*s1*s3 - s2**3 - s1**2*s4 - n*s3**2
b0 = (s5*s2*s4 + s6*s3*s2 + s7*s1*s3 - s7*s2*s2 - s6*s1*s4 - s5*s3*s3)/z
b1 = (n*s6*s4 + s1*s7*s2 + s2*s5*s3 - s2*s6*s2 - s1*s5*s4 - n*s7*s3)/z
b2 = (n*s2*s7 + s1*s3*s5 + s2*s1*s6 - s2*s2*s5 - s1*s1*s7 - n*s3*s6)/
print(b0, b1, b2)
S = 0
sum = 0
xnew = [i for i in range(8)]
for i in range(8):
xnew[i] = b0 + b1 * T[i] + b2 * T[i]**2
L = abs(x[i] - xnew[i]) / x[i] * 100
sum += (x[i] - xnew[i])**2
S = math.sqrt((sum)/(n-1))
r = (sxy-sx*sy/n)/((n-1)*math.sqrt(((sx2-sx*sx/n))/(n-1))*math.sqrt(((sy2-sy*sy/n))/(n-1)))
print(T[i], x[i], round(xnew[i], 2), round(L, 2))
print(f"S = {S}")
print(f"r = {r}")
Приложение Б
7.730297618970703 0.210589880952381 -7.43630952381e-05
300 64.18000000000001 64.20999999999999 0.05
400 79.91 80.06999999999999 0.2
500 94.64 94.43000000000001 0.22
600 107.53 107.31 0.2
700 118.7 118.71 0.0
800 128.37 128.61 0.19
900 136.82 137.03 0.15
1000 144.18 143.96 0.15
S = 0.1947301027709185
r = 0.9915612942641659
Приложение В
import math
T = [300, 400, 500, 600, 700, 800, 900, 1000]
x = [20.33, 15.73, 11.72, 8.28, 5.48, 3.22, 1.46, 0.17]
numbers = 8
s1 = 0
s2 = 0
s3 = 0
s4 = 0
s5 = 0
s6 = 0
s7 = 0
s8 =0
sxy = 0
sx = 0
sy = 0
sx2 = 0
sy2 = 0
n = 8
for i in range(8):
s1 += T[i]
s2 += T[i]**2
s3 += T[i]**3
s4 += T[i]**4
s5 += x[i]
s6 += (x[i] * T[i])
s7 += (T[i]**2 * x[i])
s8 = s8 + T[i]**2
sxy=(sxy+T[i]*x[i])
sy=(sy+x[i])
sx=(sx+T[i])
sx2=(sx2+(T[i])**2)
sy2=(sy2+(x[i])**2)
z = n*s2*s4 + s1*s3*s2 + s2*s1*s3 - s2**3 - s1**2*s4 - n*s3**2
b0 = (s5*s2*s4 + s6*s3*s2 + s7*s1*s3 - s7*s2*s2 - s6*s1*s4 - s5*s3*s3)/z
b1 = (n*s6*s4 + s1*s7*s2 + s2*s5*s3 - s2*s6*s2 - s1*s5*s4 - n*s7*s3)/z
b2 = (n*s2*s7 + s1*s3*s5 + s2*s1*s6 - s2*s2*s5 - s1*s1*s7 - n*s3*s6)/z
print(b0, b1, b2)
S = 0
sum = 0
xnew = [i for i in range(8)]
for i in range(8):
xnew[i] = b0 + b1 * T[i] + b2 * T[i]**2
L = abs(x[i] - xnew[i]) / x[i] * 100
sum += (x[i] - xnew[i])**2
S = math.sqrt((sum)/(n-1))
r = (sxy-sx*sy/n)/((n-1)*math.sqrt(((sx2-sx*sx/n))/(n-1))*math.sqrt(((sy2-sy*sy/n))/(n-1)))
print(T[i], x[i], round(xnew[i], 2), round(L, 2))
print(f"S = {S}")
print(f"r = {r}")
Приложение г
37.29636904761701 -0.06508630952380952 2.80178571429e-05
300 20.33 20.29 0.19
400 15.73 15.74 0.09
500 11.72 11.76 0.32
600 8.279999999999999 8.33 0.62
700 5.48 5.46 0.28
800 3.22 3.16 1.9
900 1.46 1.41 3.21
1000 0.17 0.23 34.07
S = 0.04661409818563231
r = -0.9814003642834355
По зависимости диаметра капель от расхода смеси сняли значения и построили график. В результате наилучшим образом описываются значения полиноминальной функцией 4 порядка. Степень близости составила 1.