Using R for Linear Regression

In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional entries (all current as of version R-2.4.1). Sample texts from an R session are highlighted with gray shading. Suppose we prepare a calibration curve using four external standards and a reference, obtaining the data shown here: The expected model for the data is signal = β o + β 1 ×conc where β o is the theoretical y-intercept and β 1 is the theoretical slope. The goal of a linear regression is to find the best estimates for β o and β 1 by minimizing the residual error between the experimental and predicted signal. The final model is signal = b o + b 1 ×conc + e where b o and b 1 are the estimates for β o and β 1 and e is the residual error. To complete a linear regression using R it is first necessary to understand the syntax for defining models. Let's assume that the dependent variable being modeled is Y and that A, B and C are independent variables that might affect Y. The general format for a linear 1 model is response ~ op1 term1 op2 term 2 op3 term3… 1 When discussing models, the term 'linear' does not mean a straight-line. Instead, a linear model contains additive terms, each containing a single multiplicative parameter; thus, the equations y = β 0 + β 1 x y = β 0 + β 1 x 1 + β 2 x 2 y = β 0 + β 11 x 2 y = β 0 + β 1 x 1 + β 2 log(x 2) are linear models. The equation y = αx β , however, is not a linear model.