RT Book, Section
A1 Glantz, Stanton A.
A1 Slinker, Bryan K.
A1 Neilands, Torsten B.
SR Print(0)
ID 1141902428
T1 Nonlinear Regression
T2 Primer of Applied Regression and Analysis of Variance, 3e
YR 2017
FD 2017
PB McGraw-Hill Education
PP New York, NY
SN 9780071824118
LK accessbiomedicalscience.mhmedical.com/content.aspx?aid=1141902428
RD 2022/01/22
AB The multiple linear regression and analysis of variance models predict the dependent variable as a weighted sum of the independent variables. The weights in this sum are the regression coefficients. In the simplest case, the dependent variable changed in proportion to each of the independent variables, but it was possible to describe many nonlinear relationships by transforming one or more of the variables (such as by taking a logarithm or a power of one or more of the variables), while still maintaining the fact that the dependent variable remained a weighted sum of the independent variables. These models are linear in the regression parameters. The fact that the models are linear in the regression parameters means that the problem of solving for the set of parameter estimates (coefficients) that minimizes the sum of squared residuals between the observed and predicted values of the dependent variable boils down to the problem of solving a set of simultaneous linear algebraic equations in the unknown regression coefficients. There is a unique solution to each problem and the coefficients can be computed for any linear model from any set of data. Moreover, because the coefficients are themselves weighted sums (more precisely, linear combinations) of the observations, statistical theory demonstrates that the sampling distributions of the regression coefficients follow the t or z distributions, so that we can conduct hypothesis tests and compute confidence intervals for these coefficients and for the regression model as a whole. These techniques are powerful tools for describing complex biological, clinical, economic, social, and physical systems and gaining insight into the important variables that define these systems, despite the restriction that the model be linear in the regression parameters.