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[QUOTE="FactChecker, post: 6864177, member: 500115"] Suppose you are using linear regression to fit the data to the model ##y=\beta_1 x + \beta_0 + \epsilon##. If the ##x## values are known with no errors, then we know that linear regression works fine. On the other hand, suppose that the measured ##x## values have some errors and that ##X_{measured} = \alpha_1 X_{actual} + \alpha_0 + \epsilon_X##. Then linear regression would give a result like ##Y=\beta_1 X_{measured} + \beta_0 + \epsilon## ## = \beta_1(\alpha_1 X_{actual} +\alpha_0 + \epsilon_X)+ \beta_0+ \epsilon## ## = (\beta_1\alpha_1) X_{actual} + (\beta_1\alpha_0+\beta_0) + (\beta_1\epsilon_X + \epsilon)##. So it is still a valid process, but it is estimating ##Y## based on the measured ##X## value. That may be what you really want. But if you are trying to get the theoretical relationship between ##Y## and ##X_{actual}##, it might not be a good model to use. [/QUOTE]
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