# 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 h in height:
print(h)
print('\n')
for f in fev:
print(f)

```
134
138
142
146
150
154
158
162
166
170
174
178
1.7
1.9
2.0
2.1
2.2
2.5
2.7
3.0
3.1
3.4
3.8
3.9
```

# 2. Import libraries - NumPy and matplotlib
import numpy as np
from matplotlib import pyplot as plt

# 3. Plot the data; add labels to axes and plot title
plt.scatter(height,fev)
plt.xlabel('Height')
plt.ylabel('FEV')
plt.title('Height and FEV Visualized')

# 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)
n=len(height)-1
coeff=compute_int_coeff(n,height,fev)
x_eval=np.linspace(134,178,1000)
y=[]
for i in range(0,len(x_eval)):
polynomial=eval_int_polynomial(n,height,x_eval[i],coeff)
y.append(polynomial)

# 5. Plot the interpolating polynomial from a height of 134 cm to 178 cm
plt.plot(x_eval,y)
plt.title('Interpolating polynomial from 134-178')

# 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?
x=[165,175]
for i in range(len(x)):
polynomial=eval_int_polynomial(n,height,x[i],coeff)
print(f'Height :{x[i]} FEV {polynomial}')
#I would say the general better prediction would be the 165 because the data changes trend towards the end which may skew the prediction

```
Height :165 FEV 3.1044129974208774
Height :175 FEV 3.3490242131985744
```

# 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(x,y)
plt.title('Piecewise Linear polynomial Interpolating')
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
x=np.linspace(165,176)
y=np.interp(x,height,fev)
print(f'Height:{x[0]} FEV:{y[0]}')
print(f'Height:{x[-1]} FEV:{y[-1]}')
#This predicted lower for 165 and much higher for 176 than the other model

```
Height:165.0 FEV:3.075
Height:176.0 FEV:3.8499999999999996
```