# Creating functions to calculate the sum of squares
def ssXY(x, y):
    """Calculates the Sum of Squares for 'x' and 'y'."""
    n = y.size
    return sum(x*y) - ((sum(x)*sum(y))/n)


def ssXX(x):
    """Calculates the Sum of Squares for 'x'."""
    n = x.size
    return sum(x*x) - ((sum(x)*sum(x))/n)

# Finding/Printing the value of the slope, intercept, and the RMSE to csv
slope = ssXY(features_DSH, Target_DSH)/ssXX(features_DSH)
intercept = Target_DSH.mean() - slope * features_DSH.mean()
slope_ = 'The slope is:'
intercept_ = 'The intercept is:'
outputDF = pd.DataFrame.from_dict({slope_:[slope], intercept_: [intercept],
                                   'RMSE:': np.sqrt(metrics.mean_squared_error(Target_DSH, predict_Linear))})

# Writing to file
counter = 1
filepath = '/Users/Chris/Documents/Programming_Practice/gistHub/slrVIZ_' + str(counter) + '.csv'
with open(filepath, 'w') as f:
    outputDF.to_csv(path_or_buf= f)

# Printing the value of the slope, intercept, and the RMSE to csv
print(slope_, " ", slope, ' and ', intercept_, " ", intercept)
print('\nRMSE: ', np.sqrt(metrics.mean_squared_error(Target_DSH, predict_Linear)))


# Plotting the points in a scatter plot
plt.figure(figsize= (10, 5))
plt.scatter(features_DSH, Target_DSH,marker='*',color = '#1f77b4');

# Plotting the model
plt.plot(features_DSH, slope* features_DSH + intercept, color = 'k')
plt.title('Linear Regression Model')
plt.xlabel('Features')
plt.ylabel('Target');