I am getting positive slope for one sample and negative slope for another sample.Generally when do we get positive slope and when do we get negative slope?
Jasper -
First, plotting your data was a very good idea. You have a lot of information, just from that. Scatterplots are very informative.
Are you saying that W and H are linearly related? (What are W and H?) You mentioned slope, but did you mean these are linearly related variables, or are you referring to instantaneous slopes on a nonlinear curve? Which is the y-value? Just curious. Regardless, a positive slope to the regression line (or to a tangential line) would mean an estimated positive correlation between y and x. A negative slope would mean a negative correlation. If you are getting positive b one time and negative b another, then results are not conclusive, and/or you have made an experimental error.
If these are linear equations, what are your estimated b and estimated standard error of b in each case? It is always important to obtain estimate standard errors for your estimated regression coefficients. Also, you can obtain an estimate for the "variance of the prediction error," to get an idea of error in y, but remember that measurement error can throw off everything. (The variance of the prediction error is found in econometrics books, and/or I could point out an estimator in one or more of my papers on RG. Also, it's square root is SDSI in SAS PROC REG, and I would imagine available in other software, and I have an excel file or two on RG that might help.)
Cheers - Jim
Perhaps the estimated values for the slopes in your two sets of experiments are not large compared to their estimated standard errors, so that W and H (whatever they are) may basically not be correlated, or are very weakly correlated, such that neither is a good 'predictor' for the other.
What are your sample sizes in each experiment? Sample size and variance are each important. If the sample size is too small and/or variance too high, you may not learn much. If the sample size is too large, you may increase measurement error, which will increase variance.
β= 4ε tanθ
The method to separate the contributions of particle size and microstrain to the line broadening in the XRPD patterns is the Williamson–Hall (WH) plotting.
read more on this paper: "Materials Letters 72 (2012) 36–38"
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