Simple Linear Regression for Homoscedastic Data

In statistical theory regression analysis refers to procedures used to model relationships between variables and determine the magnitude of those relationships so that the quantified models can be used to make predictions. Regression analysis models the relationship between one 

In analytical chemistry we always try to arrange that Equation [8.19a] provides an adeqnate model for the relationship between the instrumental response (Y) and the concentration (or amount) of analyte (x) injected directly into the instrument (instrumental cahbration) or used to spike a blank matrix (method calibration, see Section 8.5). When analytical chemists speak of a linear calibration equation they refer to Equation [8.19a], a simple linear regression model that is linear in both the fitting parameters and also in the independent variable Equation [8.19b] might be referred to as a non-linear calibration equation by a chemist, although to a statistician it is an example of a simple linear regression model, i.e., it is hnear in aU of the fitting parameters. 

Eqnation [8.19a] is desirable for several reasons only two fitting parameters need to be calculated, it is straightforward to invert the equation so as to calculate an 

One other restriction applies to the following expressions for A and B and related parameters, namely, the data are assumed to be homoscedastic, i.e., the reproducibilities of Y (given by standard deviations s(Yj), Equation [8.2c]) 

Legendre and Gauss the Birth of Least-Squares Regression 

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