Statistics and Analysis of Scientific Data by Massimiliano Bonamente

Author:Massimiliano Bonamente
Language: eng
Format: epub, pdf
Publisher: Springer New York, New York, NY

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8.8 Use the data provided in Table 6.​1 to calculate the best-fit parameters a and b for the fit to the radius vs. pressure ratio data, and the minimum χ 2. For the fit, you can assume that the radius is known exactly, and that the standard deviation of the pressure ratio is obtained as a linear average of the positive and negative errors.

8.9 Show that, when all measurement errors are identical, the least squares estimators of the linear parameters a and b are given by b = Cov(X, Y )∕Var(X) and a = E(Y ) − bE(X).

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