Hi! I am working on a linear regression model where both my x and y values contain errors. In fact, they are repeated measurements of the same samples -- I am doing this to see if the measuring device is working properly. I found least square fitting formulas at
http://mathworld.wolfram.com/LeastSquaresFitting.html and also I found maximum likihood estimate formulas for variables both containing errors on a book by Forman S.Acton -- Analysis of Straight Line Data. I am getting approximately correct results, but I am wondering if there is a way to find out what the variance and standard deviation of the regression parameters are. For example, if in my y=mx+b equation, m is found to be .9678, could I somehow find the confidence interval for the slope? I have the book Mathematical Statistics: Basic Ideas and Selected Topics by Peter Bickel at hand but the reading is giving me a lot of headaches.... I greatly appreciate your help : ) Thanks! Shirley. Hi! I am not sure if my previous message is clear enough... here is part of my data: 834.0 804.0 1061.0 1019.0 466.0 446.0 531.0 514.0 1037.0 1006.0 634.0 614.0 390.0 377.0 504.0 508.0 546.0 516.0 569.0 547.0 655.0 630.0 704.0 665.0 714.0 698.0 1181.0 1128.0 712.0 673.0 488.0 476.0 462.0 439.0 490.0 470.0 ...... and here is my result: Using perpendicular offsets: m = 1.0000218762548265 b = -21.93534402271200 Residuals: sum = 10598.829125279093 sumSqrt = 144880.87203048688 ---------------------------- Using maximum liklihood m = 0.9695748177645382 b = 0.2864222371090363 Residuals: sum = 7557.882289767819 sumSqrt = 97142.18567110984 I am not sure why they gave me different results either (because the perpendicular offset is supposed to minimize the sum of squares of the residuals but the second set of m and b is actually giving me smalled residual sums. If I assume the x and y variables have equal error, which is normally distributed with the expected value of 0, is there anyway of finding out the variance of the regression parameters, or the slope and the intercept? a milliam thanks :^) Shirley ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at http://jse.stat.ncsu.edu/ =================================================================
