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] n_height = len(height) n = 0 for x in range (0,n_height) : print (f"{height [n]} {fev [n]}") n = n + 1

# 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 x= height y= fev plt.plot (x,y, "b+") plt.xlabel ("Height") plt.ylabel ("FEV") plt.title ("Scatter plot of data")

# 4. Input functions to find interpolating polynomial def compute_int_coeff (n, x, y) : coeff = [n] # 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)

# 5. Plot the interpolating polynomial from a height of 134 cm to 178 cm 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] x = height y = fev n = 11 x_plt = np.linspace(134, 178, 10000) coeff = compute_int_coeff (n,x,y) y_plt= [] for i in range (0, len(x_plt)): poly = eval_int_polynomial (n, x, x_plt [i], coeff) y_plt.append (poly) print (x_plt) print (y_plt) plt.plot (x_plt,y_plt, "r") plt.plot (x,y, "g+") plt.xlabel ("Height") plt.ylabel ("Polynomial") plt.title ("Scatter plot of data")

# 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? 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] x = height y = fev n = 11 x_plt = np.linspace(165, 178, 10000) coeff = compute_int_coeff (n,x,y) y_plt= [] for i in range (0, len(x_plt)): poly = eval_int_polynomial (n, x, x_plt [i], coeff) y_plt.append (poly) print (x_plt) print (y_plt) plt.plot (x_plt,y_plt, "r") plt.plot (x,y, "g+") plt.xlabel ("Height") plt.ylabel ("Polynomial") plt.title ("Scatter plot of data") #The first graph is a better prediction because more of the points fall on the red line

# Import libraries import matplotlib.pyplot as plt import numpy as np

# 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