[Python] Quants : Beta calculation using pandas

Need help in verifying the way beta is calculated in below two ways:

beta = {
'AAPL' : (df['AAPL'].rolling(252).corr(df['QQQ'])) * (df['AAPL'].rolling(252).std() ) / (df['QQQ'].rolling(252).std()),
'AMZN' : (df['AMZN'].rolling(252).corr(df['QQQ']) * df['AMZN'].rolling(252).std() ) / (df['QQQ'].rolling(252).std()),
'GOOGL' : (df['GOOGL'].rolling(252).corr(df['QQQ']) * df['GOOGL'].rolling(252).std() ) / (df['QQQ'].rolling(252).std()),
'META' : (df['META'].rolling(252).corr(df['QQQ']) ) * (df['META'].rolling(252).std()) / (df['QQQ'].rolling(252).std()),
'NFLX' : (df['NFLX'].rolling(252).corr(df['QQQ']) * df['NFLX'].rolling(252).std() ) / (df['QQQ'].rolling(252).std()),
'QQQ' : (df['QQQ'].rolling(252).corr(df['QQQ']) * df['QQQ'].rolling(252).std() ) / (df['QQQ'].rolling(252).std()),
}

beta = pd.DataFrame(beta) beta

The solution (in course) to calculate beta is given as below:

''' corr = ret.rolling(252).corr(ret['QQQ'])
vol = ret.rolling(252).std()
beta = (corr*vol).divide(vol['QQQ'],axis=0) '''

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