ANSWERS: 2
  • Maybe there is something in these links that might help... http://www.jeremymiles.co.uk/regressionbook/extras/appendix2/excel/ http://homepage.mac.com/samchops/B733177502/C1517039664/E20061125110330/index.html
  • I can tell you about 'r' the coefficient of regression. (RSQ is probably the square of that). Suppose your data values are x[i] and y[i] Suppose you denote the sum over i of x[i]*y[i] as Sxy Then if the x[i] and y[i] have mean of zero, the line of best fit is given by y_fit = (Sxy/Sxx) x (you can arrange for the x[i] and y[i] to have a mean of zero by subtracting the mean x from each x[i] and the same for y before you start) So how good is the fit? Well we might want to find out what the root mean square error is: the square root of the average value of (y - y_fit)^2 = sqrt(sum over i (y[i] - y_fit[i])) = sqrt(sum over i (y[i] -(Sxy/Sxx)x[i])) = sqrt(Syy - (Sxy)^2/Sxx) Take a factor of sqrt(Syy) out : = sqrt(Syy) sqrt(1 - (Sxy)^2/(Sxx Syy)) The sqrt(Syy) part depends only on the scale of the y coordinates. Divide all the y coordinates by this and it would disappear. I take r, the correlation coefficient, from the second bit: r = Sxy/sqrt(Sxx Syy) r runs from -1 to 1 r=-1 and describes a perfect linear relationship with a negative slope (example y=-3x+2) r=0 describes no linear relationship at all: (example: y = 3x^2 with points taken symmetrically) r=1 describes a perfect linear relationship with a positive slope (example y=x-2) I don't have "Multiple R" on my ancient copy of Excel, so I'm not sure about that, but it might be that you go through the same analysis for several variables, and use the formula: (y - y_fit)^2 + (z - z_fit)^2 + ...

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