REGRESSION
Regression analysis is a statistical technique for
investigating and modelling the relationship between
variables. Regression analysis is one of the two most
widely used statistical techniques (the other one is
ANOVA), and it is used in almost

MULTIPLE REGRESSION MODELS
The multiple linear regression model with k regressors
is
Y 0 1 X 1 2 X 2 . k X k
The parameters j, j =1,2,.,k are called the regression
coefficients. The parameters j represents the expected
change in the respons Y per unit ch

DIAGNOSTICS AND REMEDIAL MEASURES
INFLUENTIAL OBSERVATIONS
Point A in figure 1 is remote in the X-space from the rest of the sample, but it lies almost on the
regression line passing through the rest of the sample points. This point does not affect the es

NCSS Statistical Software
NCSS.com
Chapter 308
Robust Regression
Introduction
Multiple regression analysis is documented in Chapter 305 Multiple Regression, so that information will not be
repeated here. Refer to that chapter for in depth coverage of mult

REGRESSION IN MATRIX TERMS
Define Y to be the vector of observations yi, X to be the matrix of predictor variables, to be the
vector of parameters to be estimated, to be a vector of errors and 1 to be a vector of ones.
y1
y
2
.
Y
.
.
yn
1 x1
1

ROBUST REGRESSION
Robust regression methods are used when the distribution of the response
variable is considerably non-normal and/or there are outliers that affect the
regression model. The outliers may have a strong influence on the method of
least squa

Tests for Heteroscedasticity
There are several formal tests that can be used to test for the assumption that the
residuals are homoscedastic in a regression model. White's (1980) test is general
and does not presume a particular form of heteroscedasticity

POLYNOMIAL REGRESSION MODELS
Polynomial models are widely used in situations where the response is curvilinear. They are also
useful as approximating functions to unknown and possibly very complex non-linear relationships. A
second order polynomial regres

MULTICOLLINEARITY
The use and interpretation of a multiple regression model often depend explicitly or implicitly on the
estimates of the individual regression coefficients. The inferences that are frequently made include:
a. Identifying relative effects

REGRESSION
Regression analysis is a statistical technique for
investigating and modelling the relationship between
variables. Regression analysis is one of the two most
widely used statistical techniques (the other one is
ANOVA), and it is used in almost

Handout for Statistics 416: Statistical Design and Analysis
of Microarray and RNA-seq Experiments
Lowess and Loess: Local Regression Smoothing
The names "lowess" and "loess" are derived from the term "locally weighted scatter plot
smooth," as both methods

Classification and Regression Trees
Introduction
Regression Trees
Classification Trees
Summary
Skills Practice
Reference Material
1
Introduction
In previous sections, we have seen how to model the
relationship between a response and predictors.
For

Tests for Heteroscedasticity
There are several formal tests that can be used to test for the assumption that the
residuals are homoscedastic in a regression model. White's (1980) test is general
and does not presume a particular form of heteroscedasticity

VARIABLE SELECTION AND MODEL BUILDING
In most practical problems, the analyst has a large pool of possible candidate regressors, of which
only a few are likely to be important. Finding an appropriate subset of regressors for the model is
called the variab

MULTIPLE REGRESSION MODELS
The multiple linear regression model with k regressors
is
Y 0 1 X 1 2 X 2 . k X k
The parameters j, j =1,2,.,k are called the regression
coefficients. The parameters j represents the expected
change in the respons Y per unit ch

DIAGNOSTICS AND REMEDIAL MEASURES
INFLUENTIAL OBSERVATIONS
Point A in figure 1 is remote in the X-space from the rest of the sample, but it lies almost on the
regression line passing through the rest of the sample points. This point does not affect the es

NON-LINEAR REGRESSION
There are many problems in engineering and sciences where the response variable and the
predictor variables are related through a known non-linear function. This leads to a
nonlinear regression model. When the method of least squares

REGRESSION MODELS WITH AUTOCORRELATED ERRORS
SOURCE and EFFECTS of Autocorrelation
Regression models using time series data occur often in economics, business and in many fiels
of engineering. The assumption of uncorrelated or independent errors for time

POLYNOMIAL REGRESSION MODELS
Polynomial models are widely used in situations where the response is curvilinear. They are also
useful as approximating functions to unknown and possibly very complex non-linear relationships. A
second order polynomial regres

MULTICOLLINEARITY
The use and interpretation of a multiple regression model often depend explicitly or implicitly on the
estimates of the individual regression coefficients. The inferences that are frequently made include:
a. Identifying relative effects

DATA TRANSFORMATIONS
Transformations are an extremely important part of
regression analysis. Transformations are made for essentially
four purposes: (1) to transform a non-linear model into a
linear model, (2) to transform X and/or Y in such a way that
th

DATA TRANSFORMATIONS
Transformations are an extremely important part of
regression analysis. Transformations are made for essentially
four purposes: (1) to transform a non-linear model into a
linear model, (2) to transform X and/or Y in such a way that
th