问计算学院化的删除残差和outlier_test()以预测OLS

EN

def internally_studentized_residual(X,Y,y_hat):
    """

    Calculate studentized residuals internal

    Parameters
    ______________________________________________________________________

    X:            List
                  Variable x-axis

    Y:            List
                  Response variable of the X 


    y_hat:        List
                  Predictions of the response variable with the given X

    Returns
    ______________________________________________________________________

    Dataframe :   List
                  Studentized Residuals   


    """

#     print(len(Y))
    X = np.array(X, dtype=float)
    Y = np.array(Y, dtype=float)
    y_hat = np.array(y_hat,dtype=float)
    mean_X = np.mean(X)
    mean_Y = np.mean(Y)
    n = len(X)

#     print(X.shape,Y.shape,y_hat.shape)

    residuals = Y - y_hat

    X_inverse = np.linalg.pinv(X.reshape(-1,1))[0]
    h_ii = X_inverse.T * X

    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,y_hat):
    """

    Calculate studentized residuals external

    Parameters
    ______________________________________________________________________

    X:            List
                  Variable x-axis

    Y:            List
                  Response variable of the X 


    y_hat:        List
                  Predictions of the response variable with the given X

    Returns
    ______________________________________________________________________

    Dataframe :   List
                  Studentized Residuals External  


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


def outlier_test(X,Y,y_hat,alpha=0.1):
    """

    outlier test for the points

    Parameters
    ______________________________________________________________________

    X:            List
                  Variable x-axis

    Y:            List
                  Response variable of the X 


    y_hat:        List
                  Predictions of the response variable with the given X

    alpha:        float
                  alpha value for multiple test

    Returns
    ______________________________________________________________________

    Dataframe :   studentized, unadjusted p values and benferroni multiple 
                  test dataframe  


    """
    resid = deleted_studentized_residual(X,Y,y_hat)
    df = len(X) - 1 
    p_vals = stats.t.sf(np.abs(resid),df) * 2
    bonf_test = multipletests(p_vals,alpha,method="bonf")
    df_result = pd.DataFrame()
    df_result.loc[:,"student_resid"] = resid
    df_result.loc[:,"unadj_p"] = p_vals
    df_result.loc[:,"bonf(p)"] = bonf_test[1]
    df_result.index = X.index

    return df_result