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1362 Pre-laboratory Aetivity for Coefficient of Linear Expansion Refer to: EIU Physies Department Laboratory Manual SP 2003, EIU Department of Physics and An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements 2d ed.. John R. Taylor. University Science Books, CA, 1997 Review of Least Squares Fit to a Line We often search for linear relationships between variables. In PHY 1352 the method of least squares was used as a technique to find the best-fit line to data. This method was introduced by utilizing the notion o finding the least, or smallest error, of a linear fit to data. The idea derivative and setting it equal to zero. Recall that squaring this distance forces all the errors to be positive which allows us to make sense of statistical averaging. We introduce the idea here to repeatable and quantifiable method of fitting data to a line. We wish to define a distance function between the is to minimize the error distance by taking a establish a transparent, line and each data point and then select a slope and intercept so this function is minimized. Chapter 8 Taylor, p. 182, is devoted to finding the expressions for the slope and intercept for the best fit, Eqs. 8.10, 8.11, 8.12, p. 184; here we shall practice using it with a data set. Let S l(x, y)1,2,3. measurements and y A B x then Consider data collected for measuring the linear coefficient of expansion for a uniform solid. Measurements are of the linear expansion from equilibrium, AL, in meters, and the temperature from equilibrium, ΔΤ in Kelvins, ordered pairs given by (x, y)>(AT K, AL m). Consider data of the form: N-3, (5.8, 0.000017), (13.4,0.000036), (21.6, 0.000048) from this data find:

Answer 1