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

# Input exact values for comparison # dutch_man_1925 = 174.83; us_man_1925 = 174.53 dutch_man_1955 = 180.23; us_man_1955 = 177.22 dutch_man_1995 = 182.54; us_man_1995 = 177.16 # dutch_woman_1925 = 162.2; us_woman_1925 = 160.97 dutch_woman_1955 = 167.11; us_woman_1955 = 163.54 dutch_woman_1995 = 168.73; us_woman_1995 = 163.56

# Read in the data and plot; add axes labels, plot title and legend # Note: to add legend use label option in plt.plot (e.g., label='Dutch Men') and then use # the command plt.legend () # filename = 'human_heights.txt' dutch = np.loadtxt(filename, usecols=1, skiprows=2) print (dutch) us = np.loadtxt(filename, usecols=3, skiprows=2) print (us) plt.plot (dutch, 'ro') plt.plot (us, 'bo') plt.xlabel ("Year") plt.ylabel ("Average Weight") plt.title ("Weight of Dutch Men vs US Men") plt.legend ("Dutch USA") plt.show()

# Linear regression fit for both Dutch and U.S.; plot and print out the line line_coeff = np.polyfit(dutch,us,1) print (line_coeff) print(f"The equation of the line using linear regression is {line_coeff[0]}x \ +{line_coeff[1]}") plt.plot(dutch, us, 'ro') plt.xlabel("Dutch Men") plt.ylabel("US Men") dmin=np.min(dutch); dmax = np.max(dutch) xx=np.linspace (dmin, dmax ) f= np.poly1d(line_coeff) yy=f(xx) plt.plot(xx,yy,'b') plt.title("Linear Regression fit to data") plt.show()

# Calculate the variance for each fit; use the function that we wrote in a previous notebook def calculate_variance ( x, y,coeff): # # Input: the x and y arrays for the data points, coefficients of line found using LR # # Output: variance # n=len(x) degree = len(coeff) -1 var = 0.0 for i in range(0,n) : if (degree == 1 ) : y_line = coeff[0] * x[i] + coeff[1] # calculate value of y on line for given x[i] else : y_line = coeff[0] * x[i]*x[i] + coeff[1] *x[i] + coeff[2] y_data = y[i] # y height of data point at x[i] distance = y_data-y_line var = var + distance * distance var = ( var )/ float(n) return (var) var = calculate_variance(dutch, us,line_coeff) print(' The variance of the linear fit to data is',var) # # Input: the x and y arrays for the data points, coefficients of line found using LR # # Output: variance #

# Quadratic regression fit for Dutch and U.S.; plot and print out the parabolas parabola_coeff = np.polyfit(dutch,us,2) print(f"The equation of the parabola using regression is {parabola_coeff[0]}x^2 \ +{parabola_coeff[1]}x + {parabola_coeff[2]}") plt.plot(dutch, us, 'ro') # scatter plot of data plt.xlabel("Dutch Men") plt.ylabel("US Men") # # Create data to plot parabola dmin=np.min(dutch); dmax = np.max(dutch) xx=np.linspace (dmin, dmax ) g= np.poly1d(parabola_coeff) yy=g(xx) plt.plot(xx,yy,'b') plt.title("Quadratic Regression fit to data") plt.show()

# Calculate variance for the quadratic fits var_quad = calculate_variance(dutch, us, parabola_coeff) print("The variance for a quadratic fit to data is", var_quad)

# Use best fit to predict average heights in 1955 and 1995 for both Dutch and U.S.; compute percent error; # round values to 2 decimal places # predicted_linear = f(0) # remember we set f = poly1d for linear case predicted_quad = g(1) # remember we set g = poly1d for parabolic case print(f"The predicted value at 1955 using the linear fit is {predicted_linear}\ and using a quadratic fit is {predicted_quad}") print(f"The difference in the predicted values is {predicted_linear -predicted_quad}")