def internally_studentized_residual(X,Y):
    X = np.array(X, dtype=float)
    Y = np.array(Y, dtype=float)
    mean_X = np.mean(X)
    mean_Y = np.mean(Y)
    n = len(X)
    diff_mean_sqr = np.dot((X - mean_X), (X - mean_X))
    beta1 = np.dot((X - mean_X), (Y - mean_Y)) / diff_mean_sqr
    beta0 = mean_Y - beta1 * mean_X
    y_hat = beta0 + beta1 * X
    residuals = Y - y_hat
    h_ii = (X - mean_X) ** 2 / diff_mean_sqr + (1 / n)
    Var_e = math.sqrt(sum((Y - y_hat) ** 2)/(n-2))
    SE_regression = Var_e*((1-h_ii) ** 0.5)
    studentized_residuals = residuals/SE_regression
    return studentized_residuals

def deleted_studentized_residual(X,Y):
    #formula from https://newonlinecourses.science.psu.edu/stat501/node/401/
    r = internally_studentized_residual(X,Y)
    n = len(r)
    return [r_i*math.sqrt((n-2-1)/(n-2-r_i**2)) for r_i in r]