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# MODERN PHYSICS LAB PHYS 431

UW

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This 7 page Class Notes was uploaded by Dr. Simeon Wiza on Wednesday September 9, 2015. The Class Notes belongs to PHYS 431 at University of Washington taught by Staff in Fall. Since its upload, it has received 7 views. For similar materials see /class/192444/phys-431-university-of-washington in Physics 2 at University of Washington.

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Date Created: 09/09/15

PHYSICS 331 NOTES ON lVHCROSOFT EXCEL LINEST 27 March 2005 A detailed description of how to calculate a least squares fit to a straight line is given in Chapter 6 of Bevington and Robinson with a summary on p l 14 for the case where the y values have different precisions as in Fig 62 and the x value are precise The programs described there are available along with two errata for the book p3 and p12 at wwwmhhe combevington A much simpler algorithm can be used if all the y values have the same precision as in Fig 61 and is available through the function linest in Microsoft Excel The following pages are from wwwcolby educhemist PChemnoteslinestpdf This is a document dated 20 August 2002 which explains how to get estimates of statistical uncertainties in slope and intercept along with results for least squares fitting using Excel on either Mac or PC It is interesting to note that versions of Excel before 2003 actually gave incorrect results when the curve was constrained to go through the origin andor some data were collinear Excel 2002 and earlier versions always return results that are not correct when the intercept argument is set to FALSE LINEST has been greatly improved for Excel 2003 If you use an earlier version of Excel verify that predictor columns are not collinear before you use LINEST Predictor columns knownx s are collinear if at least one column can be expressed as a sum of multiples of others This is all explained at httpsupportmicrosoft comkb 828533 A detailed description of how to do least squares fitting using explicit formulae in Excel as well as using linest is available but it does not tell the trick for entering an array formula using a Mac at http deptphy sicsupenn eduuglabsLeast sguaresfittingwith Excelpdf was In Excel Th2 Ex 21 spreadsheet nmm Inuit is a campm 1mm ma squares Curve mung mun Lhatpmnbcesmcumnty emmates fax the tvaluas mm are m waysm access39he Inuit mummy mm m an amuym angina analyastaals m ufmaaas These m asaspzudsheetfunchm 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Haresavnn suusues whim 1W7 1W7 Step 5 NW haeis the imgm39mnt 52 LINEST 5 an array funcnun Whth means that when yuu emenhe nrmulam ehe eeumu1hp1e cellswxll beused senhe uulput quhe fuheheh Tu are hmula oh the acmmsh hem huld dawn the apple key and e c a press adds txlquot and Shu keys sh Ema quot Excel h h 51 as uwn abuve press return the pc huld duwnth 1 Highhghnng the mu funnula aha cypmg the apple key ur cmquotquotsh quot and return 15 the ehly Way m Enta sh army funnula fuheheh eeu Furexample the slupe 15 z zatn I85 and Lhexnta39ceptxs 7 an n 41 Step 6 You should now evaluate the model that you have built The r2 value is often used for this purpose but it is only a rough indicator of the goodness of t The r2 value is calculated from the total sum of squares which is the sum of the squared deviations of the original data from the mean 1391 2 tOtal SS 2 Y1 39 Yav il and the regression sum of squares which is the sum of the squared deviations of the t values from the mean 11 regression ss 2X 3 Yaw2 il G I 2 7 regression ss 7 2X 9 39 yaV2 mug r 7 total 55 7 2X Yi Yav2 Values close to one are good The uncertainties in the slope and intercept are much better for judging the quality of the t In the example the uncertainty in the slope is 00852629 100 3 and the uncertainty in the intercept is 12 which is only about two signi cant gures in each The uncertainties in the slope and intercept are not as good as the r2 of 0996 might have indicated An even better statistical test of the goodness of t is to use the Fisher Fstatistic The Fstatistic is the ratio of the variance in the data explained by the linear model divided by the variance unexplained by the model The Fstatistic is calculated from the regression sum of squares and the residual sum of squares The residual sum of squares is the sum of the squared residuals 11 1391 residual ss 2yi 902 Z riz 11 11 Dividing by the degrees of freedom gives the variance of the y values 5y Th2 gamma m names m mm m names mm mm wmanam y 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