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## metrics for regression model
def metrics_regression(y:'array',yhat:'array',k:int=None)->dict:
    """
    Metrics for regression model: BIAS, MAE, R2 / R2 adjusted. It is robust to NaN values.
    y -- array of real data (observation).
    yhat -- array of data to be scored (prediction).
    k -- number of predictors (features) for calculating R2 adjusted. If this one is None is returned R2 (default None). 
    return -- dictionary of calculated metrics.
    """
    import numpy as np
    from pandas import DataFrame

    # drop nan values
    df = DataFrame({'y':y,'yhat':yhat}).dropna()
    fcst = df.yhat.values
    obs = df.y.values
    del(df)

    # calculate general error
    error = fcst - obs 

    ## bias
    bias = np.mean(error)
    ## mae
    mae = np.mean(np.abs(error))

    ## R2 / R2 ajusted
    SS_Residual = sum((obs-fcst)**2)
    SS_Total = sum((obs-np.mean(obs))**2)
    r_squared = 1 - (float(SS_Residual))/SS_Total
    if k is None: r2 = r_squared
    else: 
        adj_r_squared = 1 - (1-r_squared)*(len(obs)-1)/(len(obs)-k-1)
        r2 = adj_r_squared

    # return
    return {'bias':bias,'mae':mae,'r2':r2}