Suppose you have a set of data points with uncertainty values for each of them. For simplifications, assume it is a linear plot. Is it possible to mathematically find out the MAX/MIN slopes of the linear plot of the data points? Is there a program that can do such analysis for you? thanks in advance
The answer to your first question is "yes". Consult a graphical analysis, data analysis textbook for details. Of the many programs out there, I have used Sigmaplot to give error analysis of slopes. I believe that the latest version also does some limited non-linear analysis provided you input a mathematical function to model.
hmmm, can you refer me to some instructions/ provide some direction, because i am quite lost with that new program. thanks
Excel can do this calculation for you. The Excel program is not a tutorial, however. It is best used by someone with some familiarity of statistics and data analysis. Use the "help" pull down menu and type in "Regression Analysis". Your OP referred to MAX/MIN slope through some data points which I have never seen presented as a method to analyze data. I am familiar with least squares residual analysis as it relates to linear regression analysis. As a chemist, my suggestion would be to look at an undergraduate Analytical Chemistry text and refer to the chapter dealing with the evaluation of analytical data. My book is "Fundamentals of Analytical Chemistry", Chapter 3, by Skoog and West, 4th edition, Philadelphia: Saunders College Publishing (1982). This type of data analysis is useful to most other branches of science such as Biology, Physics, Sociology, Public Health Administration, Political Science, etc... All of these disciplines have their own applications for this type of Statistical Analysis. A discussion of the underlying statistics of linear regression can be found at: "Statistical Methods in Research and Production", 4th ed., O.L. Davies and P.L. Goldsmith, Eds., Chapter 7, New York: Hafner Publishing Co. (1972). "Introduction to Statistical Analysis", W.J. Dixon and F.J. Massey, Jr., 3rd edition, New York: McGraw-Hill (1969). You should be able to find newer editions of books titled "Introduction to Statistics (or Statistical Analysis)" at the bookstore or you might find these examples at your local University Library.