Pearson Correlation Coefficient

• 02/28/2023 at 11:07 AM #166112
  Khaled

  In statistics, the Pearson correlation coefficient, also referred to as Pearson’s r, the Pearson product-moment correlation coefficient (PPMCC), is a measure of linear correlation between two sets of data. It is the covariance of two variables, divided by the product of their standard deviations; thus it is essentially a normalised measurement of the covariance, such that the result always has a value between −1 and 1.  https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

  The Person’s  R is not to be confused with the R2 https://www.prorealcode.com/prorealtime-indicators/r-squared-correlation-coefficient-r2/ – Coefficient of determination – which measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). https://en.wikipedia.org/wiki/Coefficient_of_determination

  There was a discussion on this topic started here , but the initiator seem to have found the solution, but didn’t post it…

  So, I’ll try…

  Pearson correlation coefficient

  //ρ (rho) = cov(x, y) / (sd(x) * sd(y)), where cov is covariance, sd(x) is the standard deviation of x, etc. // cov(x,y) = ((x - E(x) * (y - E(y) ), where E(x) is the Expected Value of x... // E(x) = average(x), the expected value is the weighted sum of the xi values, with the probabilities pi as the weights. When values of x are equiprobable, then the weighted average turns into the simple average. // sd(x) = square root (variance(x;xn)) // variance(x;xn) = (x-(average(x1;xn))^2 / n Period = 5 IF barindex>Period THEN X = close VarianceX = average[Period](SQUARE((X - average[Period](X)))) sdX = SQRT(VarianceX) Y = RSI[14](close) VarianceY = average[Period](SQUARE((Y - average[Period](Y)))) sdY = SQRT(VarianceY) covXY = average[Period]((X-average[Period](X)) * (Y-average[Period](Y))) R = covXY / (sdX * sdY) ENDIF RETURN R

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  //ρ (rho) = cov(x, y) / (sd(x) * sd(y)), where cov is covariance, sd(x) is the standard deviation of x, etc.   // cov(x,y) = ((x - E(x) * (y - E(y) ), where E(x) is the Expected Value of x...   // E(x) = average(x),  the expected value is the weighted sum of the xi values, with the probabilities pi as the weights. When values of x are equiprobable, then the weighted average turns into the simple average.   // sd(x) = square root (variance(x;xn))   // variance(x;xn) = (x-(average(x1;xn))^2 / n   Period = 5 IF barindex>Period THEN X         = close VarianceX = average[Period](SQUARE((X - average[Period](X)))) sdX       = SQRT(VarianceX)   Y         = RSI[14](close) VarianceY = average[Period](SQUARE((Y - average[Period](Y)))) sdY       = SQRT(VarianceY)   covXY     = average[Period]((X-average[Period](X)) * (Y-average[Period](Y)))   R        = covXY / (sdX * sdY)   ENDIF   RETURN R

  While this correlation coefficient R shows the correlation between two variables for the current candle, I wonder if it’s not more appropriate to measure correlation of X (say Close) of candle [P] with another variable, say RSI, of previous candle [P-1]. Meaning that one can nealry predict at least direction of X based on the result of previous candle of Y.

  The most difficult now, is to find the most appropriate Y (RSI? Stoch? Volume? or combination of a few variables? calculated on same period than X or different period? )

  Please share your thoughts or any improvment you may think of.

  @Lars Nørgaard Larsen @Nicolas @Leonida1984  @Wing @robertogozzi @ PLermite

  

  Khaled

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