### Programming R Squared

https://pythonprogramming.net/how-to-program-r-squared-machine-learning-tutorial/

Straight forward tutorial – plugging in the R^2 calculation into a function.

```
# Import Libs
from statistics import mean
import numpy as np
import matplotlib.pyplot as plt
# To set charts to save as images we need to change the default behaviour
from matplotlib import style # inport style to change default behaviour of plot
style.use('ggplot') # use ggplot
# Define values
xs = np.array([1,2,3,4,5], dtype=np.float64) # dtype lets you set the data type. Not needed for this example but useful in future
ys = np.array([5,4,6,5,6], dtype=np.float64)
# Define best fit function
def best_fit_slope_and_intercept(xs, ys): # defining function to calculate slope (m) - passing values of xs and ys
m = ( ((mean(xs)*mean(ys)) - mean(xs * ys)) / # bracket space at the start and space slash at the end allows for a carridge return in the code
((mean(xs)**2)-mean(xs**2))) ## **2 raises to the power of 2
b = mean(ys) - m*mean(xs)
return m, b
m, b = best_fit_slope_and_intercept(xs,ys)
# Define function to square error
def squared_error(ys_orig,ys_line):
return sum((ys_line - ys_orig) * (ys_line - ys_orig)) # return used with calc rather than seperately first
def coefficient_of_determination(ys_orig,ys_line):
y_mean_line = [mean(ys_orig) for y in ys_orig] # one line for loop
squared_error_regr = squared_error(ys_orig, ys_line)
squared_error_y_mean = squared_error(ys_orig, y_mean_line)
return 1 - (squared_error_regr/squared_error_y_mean)
m, b = best_fit_slope_and_intercept(xs,ys)
regression_line = [(m*x)+b for x in xs]
r_squared = coefficient_of_determination(ys,regression_line)
print(r_squared)
#plt.scatter(xs,ys)
#plt.savefig('ML_Tutorial8.png', bbox_inches='tight') #Sets the output to save an image
#plt.show() # exports the image
```