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I am trying to get a legend to appear in matplotlib in order to display an r^2 value but the legend will not display. Any help would be much appreciated.

import matplotlib.pyplot as plt

import numpy as np

from scipy import stats



# Filling in the values obtained in the real image experiment

object_distance = np.array(range(15, 66, 5))

object_distance_error = 0.1

real_image_distance = np.array([29.5, 21.0, 17.4, 15.4, 14.3, 13.7, 13.1, 13.0, 12.6, 12.3, 12.3])

real_image_distance_error = 0.1

real_image_size = np.array([3.6, 2.0, 1.4, 1.0, 0.8, 0.7, 0.5, 0.45, 0.4, 0.4, 0.35])

real_image_size_error = 0.1

real_focus = 10



inverse_obj = 1.0/object_distance

inverse_rl_img = 1.0/real_image_distance

rl_slope, rl_intercept, rl_r_value, rl_p_value, rl_std_err = stats.linregress(inverse_obj, inverse_rl_img)

rl_line = inverse_obj*rl_slope + rl_intercept

r_squared = str(round(rl_r_value**2, 4))





fig1 = plt.figure()

fig1.set_size_inches(10, 10)

plt.plot(inverse_obj, inverse_rl_img, 'o', markersize=3)

plt.plot(inverse_obj, rl_line)



plt.xlabel('$Object$ ' + r'$Distance^-$'+r'$^1$' + r' (cm' + r'$^-$' +r'$^1$' + r')')

plt.ylabel('$Image$ ' + r'$Distance^-$'+r'$^1$' + r' (cm' + r'$^-$' +r'$^1$' + r')')

plt.legend([rl_line], [r"$r^2$" + r_squared])

plt.title("Graph of 1/s vs 1/s'")

plt.show()

You are trying define the text legend and plot in the same command, change for this:

fig1 = plt.figure()

fig1.set_size_inches(10, 10)

plt.plot(inverse_obj, inverse_rl_img, 'o', markersize=3, label='rl_line')

plt.plot(inverse_obj, rl_line, label='$r^2$ + r_squared')

plt.legend()



plt.xlabel('$Object$ ' + r'$Distance^-$'+r'$^1$' + r' (cm' + r'$^-$' +r'$^1$' + r')')

plt.ylabel('$Image$ ' + r'$Distance^-$'+r'$^1$' + r' (cm' + r'$^-$' +r'$^1$' + r')')

plt.title("Graph of 1/s vs 1/s'")

plt.show()

Remember that plt.legend() is just a method which calls a legend inside the graph. To define the legend use plt.plot(label='rl_line') for example.

You can also use patches:

import matplotlib.patches as mpatches

then define e.g. red_patch:

red_patch = mpatches.Patch(color='red', label=f'ru00b2={r_squared}')

and add it in plt.legend(),

plt.legend(handles=[red_patch], ...)

you'll get something like this: