Python Project 4 - Regression - Duplicate

# Import libraries import numpy as np np.loadtxt('human_heights.txt')

# 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

import numpy as np import matplotlib.pyplot as plt 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 # Read in the data and plot; add axes labels, plot title and legend filename = "human_heights.txt" years = np.loadtxt(filename,skiprows=2, usecols= (0)) dutch_men = np.loadtxt(filename,skiprows=2, usecols=(1)) us_men = np.loadtxt(filename,skiprows=2, usecols=(3)) plt.plot(years,dutch_men, 'ro',label='Dutch Men') plt.plot(years,us_men,'go',label='U.S. Men') plt.xlabel("year") plt.ylabel("height in centimeters") plt.title ("Average Height of Dutch and US Men") plt.legend() plt.show() # Note: to add legend use label option in plt.plot (e.g., label='Dutch Men') and then use # the command plt.legend () #

# Linear regression fit for both Dutch and U.S.; plot and print out the line filename = "human_heights.txt" years = np.loadtxt(filename,skiprows=2, usecols= (0)) dutch_men = np.loadtxt(filename,skiprows=2, usecols=(1)) us_men = np.loadtxt(filename,skiprows=2, usecols=(3)) dutch_men_coeff = np.polyfit(years, dutch_men, 1) dutch_men_fit = np.polyval(dutch_men_coeff, years) us_men_coeff = np.polyfit(years, us_men, 1) us_men_fit = np.polyval(us_men_coeff, years) print('Coefficients for Dutch men fit:', dutch_men_coeff) print('Coefficients for US men fit:', us_men_coeff) plt.plot(years, dutch_men, 'o', label='Dutch men') plt.plot(years, us_men, 'o', label='US men') plt.plot(years, dutch_men_fit, '-', label='Dutch men fit') plt.plot(years, us_men_fit, '-', label='US men fit') plt.xlabel('Year') plt.ylabel('Height (cm)') plt.title('Average Height of Dutch and US Men') plt.legend() plt.show()

# Calculate the variance for each fit; use the function that we wrote in a previous notebook # Calculate variances for linear regression models import numpy as np import matplotlib.pyplot as plt def calculate_variance(x, y, coeff): filename = "human_heights.txt" years = np.loadtxt(filename,skiprows=2, usecols= (0)) dutch_men = np.loadtxt(filename,skiprows=2, usecols=(1)) us_men = np.loadtxt(filename,skiprows=2, usecols=(3)) dutch_men_var = calculate_variance(years, dutch_men, dutch_men_coeff) us_men_var = calculate_variance(years, us_men, us_men_coeff) print('Variance for Dutch men fit:', dutch_men_var) print('Variance for US men fit:', us_men_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 parabolas import numpy as np import matplotlib.pyplot as plt filename = "human_heights.txt" years = np.loadtxt(filename,skiprows=2, usecols= (0)) dutch_men = np.loadtxt(filename,skiprows=2, usecols=(1)) us_men = np.loadtxt(filename,skiprows=2, usecols=(3)) dutch_men_coeff = np.polyfit(years, dutch_men, 2) us_men_coeff = np.polyfit(years, us_men, 2) dutch_men_fit = np.polyval(dutch_men_coeff, years) us_men_fit = np.polyval(us_men_coeff, years) plt.plot(years, dutch_men, label='Dutch men') plt.plot(years, us_men, label='US men') plt.plot(years, dutch_men_fit, '-.', label='Dutch men quadratic fit') plt.plot(years, us_men_fit, '-.', label='US men quadratic fit') plt.xlabel('Year') plt.ylabel('Height (cm)') plt.title('Average Height of Dutch and US Men') plt.legend() plt.show()

# Calculate variance for the quadratic fits import numpy as np import matplotlib.pyplot as plt # load data from file filename = "human_heights.txt" years = np.loadtxt(filename,skiprows=2, usecols= (0)) dutch_men = np.loadtxt(filename,skiprows=2, usecols=(1)) us_men = np.loadtxt(filename,skiprows=2, usecols=(3)) # fit quadratic regression lines dutch_men_coeff = np.polyfit(years, dutch_men, 2) us_men_coeff = np.polyfit(years, us_men, 2) # calculate predicted values of y for each x dutch_men_pred = dutch_men_coeff[0]*years**2 + dutch_men_coeff[1]*years + dutch_men_coeff[2] us_men_pred = us_men_coeff[0]*years**2 + us_men_coeff[1]*years + us_men_coeff[2] # calculate variances dutch_men_var = np.mean((dutch_men_pred - dutch_men)**2) us_men_var = np.mean((us_men_pred - us_men)**2) print("Variance of Dutch men's height data:", dutch_men_var) print("Variance of US men's height data:", us_men_var)

# 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 # import numpy as np import matplotlib.pyplot as plt # load data from file filename = "human_heights.txt" years = np.loadtxt(filename, skiprows=2, usecols=(0)) dutch_men = np.loadtxt(filename, skiprows=2, usecols=(1)) us_men = np.loadtxt(filename, skiprows=2, usecols=(3)) # Predict average heights in 1955 and 1995 for Dutch men dutch_men_height_1955 = dutch_men_coeff[0]*1955**2 + dutch_men_coeff[1]*1955 + dutch_men_coeff[2] dutch_men_height_1995 = dutch_men_coeff[0]*1995**2 + dutch_men_coeff[1]*1995 + dutch_men_coeff[2] # Predict average heights in 1955 and 1995 for US men us_men_height_1955 = us_men_coeff[0]*1955**2 + us_men_coeff[1]*1955 + us_men_coeff[2] us_men_height_1995 = us_men_coeff[0]*1995**2 + us_men_coeff[1]*1995 + us_men_coeff[2] # Calculate percent errors dutch_men_1955_error = abs((dutch_men_height_1955 - 183.8) / 183.8) * 100 dutch_men_1995_error = abs((dutch_men_height_1995 - 182.4) / 182.4) * 100 us_men_1955_error = abs((us_men_height_1955 - 177.1) / 177.1) * 100 us_men_1995_error = abs((us_men_height_1995 - 176.1) / 176.1) * 100 # Round results to 2 decimal places dutch_men_height_1955 = round(dutch_men_height_1955, 2) dutch_men_height_1995 = round(dutch_men_height_1995, 2) us_men_height_1955 = round(us_men_height_1955, 2) us_men_height_1995 = round(us_men_height_1995, 2) dutch_men_1955_error = round(dutch_men_1955_error, 2) dutch_men_1995_error = round(dutch_men_1995_error, 2) us_men_1955_error = round(us_men_1955_error, 2) us_men_1995_error = round(us_men_1995_error, 2) # Print results print("Predicted average height for Dutch men in 1955: ", dutch_men_height_1955, " cm") print("Predicted average height for Dutch men in 1995: ", dutch_men_height_1995, " cm") print("Predicted average height for US men in 1955: ", us_men_height_1955, " cm") print("Predicted average height for US men in 1995: ", us_men_height_1995, " cm") print("Percent error in predicting average height for Dutch men in 1955: ", dutch_men_1955_error, " %") print("Percent error in predicting average height for Dutch men in 1995: ", dutch_men_1995_error, " %") print("Percent error in predicting average height for US men in 1955: ", us_men_1955_error, " %") print("Percent error in predicting average height for US men in 1995: ", us_men_1995_error, " %")