# 1. Print out data in columns
height = [134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178]
fev = [1.7, 1.9, 2., 2.1, 2.2, 2.5, 2.7, 3.,3.1, 3.4, 3.8, 3.9]
for i in range(len(height)):
print(f"{height[i]} {fev[i]}")
# 2. Import libraries - NumPy and matplotlib
import numpy as np
import matplotlib.pyplot as plt
# 3. Plot the data; add labels to axes and plot title
plt.scatter(height, fev)
plt.title("FEV and Height")
plt.xlabel("Height")
plt.ylabel("FEV")
# 4. Input functions to find interpolating polynomial
def compute_int_coeff (n, x, y) :
coeff = [] # initialize list
for i in range (0,n+1): # loop to calculate n+1 coefficients
numerator = y[i]
denominator = 1. # because denominator is a product we must initialize to 1
for j in range (0,n+1):
if ( i != j) : # denominator is product of all terms except
# when x_i=x_j which would give 0
denominator = denominator * (x[i] - x[j])
coeff.append (numerator / denominator) # add term to list
return (coeff)
#
#
def eval_int_polynomial (n, x, x_eval, coeff) :
my_sum = 0. # formula is sum of n+1 terms so initialize
for i in range (0,n+1) : # loop to form sum of terms
product = 1. # initialize product in numerator of L_i
for j in range (0, n+1) : # loop to form product of terms in numerator
if ( i != j ) : # include all terms except when i = j
product = product * (x_eval - x[j])
# when this j loop is complete we have the numerator of L_i for one term
yi_times_Li = product * coeff[i] # multiplies numerator times C_i (y_i/ product)
my_sum = my_sum + yi_times_Li # keeps running tally of sum of terms
return (my_sum)
i = len(height)-1
coefficient = compute_int_coeff(n,height,fev)
x = np.linspace(134,178,1000)
answer1 = []
for i in range(0,len(x)):
answer2 = eval_int_polynomial(n,height,x[i],coefficient)
answer1.append(answer2)
print(answer1)
# 5. Plot the interpolating polynomial from a height of 134 cm to 178 cm
plt.plot(x,answer1)
plt.plot(height,fev,"ro")
# 6. Use the polynomial to predict the FEV for a height of 165 cm and of 175 cm.
# Which do you think is a better prediction?
x2 = [165,175]
answer3 = []
for i in range(len(x2)):
answer2 = eval_int_polynomial(n,height,x2[i],coefficient)
answer3.append(answer2)
print(answer3)
plt.plot(x,answer1)
plt.plot(x2,answer3,'ro')
plt.xlabel("Height")
plt.ylabel("FEV")
#I think this plot is a better prediction
# Import libraries
import matplotlib.pyplot as plt
import numpy as np
# Plot piecewise linear interpolating polynomial and data; use
x = np.linspace(134, 178)
y = np.interp(x,height,fev)
plt.plot(height,fev,'ro')
plt.plot(x,y)
plt.xlabel("Height")
plt.ylabel("FEV")
# Use the piecewise polynomial to predict the FEV for a height of 165 cm and of 176 cm.
# How does this compare with 11th degree polynomial which predicted 3.104 for 165 cm and
# 2.697 for 176 cm
x2 = np.linspace(165,176)
y2 = np.interp(x2,height,fev)
plt.plot(height,fev,'ro')
plt.plot(x2,y2)
plt.xlabel("Height")
plt.ylabel("FEV")