#Import Linear Regression model from scikit-learn.
from sklearn.linear_model import LinearRegression
def linear_regression(data, power, models_to_plot):
    #initialize predictors:
    predictors=['x']
    if power>=2:
        predictors.extend(['x_%d'%i for i in range(2,power+1)])
    
    #Fit the model
    linreg = LinearRegression(normalize=True)
    linreg.fit(data[predictors],data['y'])
    y_pred = linreg.predict(data[predictors])
    
    #Check if a plot is to be made for the entered power
    if power in models_to_plot:
        plt.subplot(models_to_plot[power])
        plt.tight_layout()
        plt.plot(data['x'],y_pred)
        plt.plot(data['x'],data['y'],'.')
        plt.title('Plot for power: %d'%power)
    
    #Return the result in pre-defined format
    rss = sum((y_pred-data['y'])**2)
    ret = [rss]
    ret.extend([linreg.intercept_])
    ret.extend(linreg.coef_)
    return ret