Week 8 Practice Notebooks - Duplicate

# 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)

# 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

# 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