# Importing Necessary Libraries
#%matplotlib inline
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = (20.0, 10.0)

# Reading Data
data = pd.read_csv('headbrain.csv')
print(data.shape)

# Collecting X and Y
X = data['Head Size(cm^3)'].values
Y = data['Brain Weight(grams)'].values


# Mean X and Y
mean_x = np.mean(X)
mean_y = np.mean(Y)

# Total number of values
m = len(X)

# Using the formula to calculate b1 and b2
numer = 0
denom = 0
for i in range(m):
    numer += (X[i] - mean_x) * (Y[i] - mean_y)
    denom += (X[i] - mean_x) ** 2
b1 = numer / denom
b0 = mean_y - (b1 * mean_x)

# Plotting Values and Regression Line

max_x = np.max(X) + 100
min_x = np.min(X) - 100

# Calculating line values x and y
x = np.linspace(min_x, max_x, 1000)
y = b0 + b1 * x

# Ploting Line
plt.plot(x, y, color='#58b970', label='Regression Line')
# Ploting Scatter Points
plt.scatter(X, Y, c='#ef5423', label='Scatter Plot')

plt.xlabel('Head Size in cm3')
plt.ylabel('Brain Weight in grams')
plt.legend()
plt.show()


# Calculating Root Mean Squares Error
rmse = 0
for i in range(m):
    y_pred = b0 + b1 * X[i]
    rmse += (Y[i] - y_pred) ** 2
rmse = np.sqrt(rmse/m)
print(rmse)