Stat 3521: Regression
Multiple Linear Regression
Feb 24, 2011
Example
Data were collected to check whether the presence of Urea
Formaldehyde Foam Insulation (UFFI) has an eect on the
ambient formaldeh
SW388R6
Data Analysis
and
Computers I
Slide 1
Testing Assumptions of Linear
Regression
The four assumptions of regression
The assumption of linearity
The assumption of
homoscedasticity
The assumption
CRITICAL THINKING SKILLS- LOGISTIC REGRESSION
Model
( log ( 1 )= 0 + 1 x 1 k x k +
Fitting regression line/least-squares line
log (
^
)= ^ 0 + ^ 1 x 1 ^ k x k
1^
0 , 1 , , k - coefficients
Questions
STAT 3521: Assignment 1 - Due February 5, 2009
(You may use MINITAB, SPLUS, SAS or OTHER SOFTWARE)
1. Consider the simple linear regression model
yi = 0 + 1 xi + i , i = 1, 2, 3, . . . , n,
where i N(
Stat 3521: Regression
Multiple Linear Regression
Feb 3, 2010
Multiple Linear Regression
Suppose that yield of a chemical process depends on
temperature and the catalyst concentration.
A multiple linea
Stat 3521: Regression
Multiple Linear Regression
Feb 9 & 10, 2010
Matrix Approach to Simple Linear Regression
We will consider the simple linear regression model
y = 0 + 1 x +
The n observations of th
Stat 3521: Regression
Special Cases of Simple Linear Regression
1 Feb, 2011
An Alternative form of the Regression Model
There is an alternative form of the simple linear regression
model that occasion
Stat 3521: Regression
Introduction to Regression Analysis
Jan 11, 2011
Introduction
Regression modeling is a statistical technique for investigating
and modeling the relationship between variables
Reg
Stat 3521: Regression
Simple Linear Regression
Jan 13, 2011
Introduction
Simple linear regression model is a model with single
regressor x that has a relationship with a response y (i.e.
straight line
Stat 3521: Regression
Simple Linear Regression
Jan 18, 2011
Fitted Values & Residuals
The expression 0 + 1 xi is called the tted value corresponds
to the ith observation with xi as the value for the e
Stat 3521: Regression
Model Adequacy Checking
March 23 & 24, 2010
R-codes for Regression
lm - #to t the model
t = lm(y x1 + x2 + x3, data=mydata)
summary(t) # show results
# Other useful functions
coe
Stat 3521: Regression
Model Adequacy Checking
March 16 & 17, 2010
Inroduction
We now know most of the basic theory for regression models
with multiple explanatory variables.
Given a specic set of data
Stat 3521: Regression
Simple Linear Regression
Jan 26 & 27, 2010
Properties of Least Square Estimates
We can rewrite the LSE of 1 as
n
1 =
ci yi
i=1
where ci = (xi x )/sxx are constants and
sxx = n (x
STATISTICS 3521
REGRESSION
ST 3521: Regression
Regression analysis is a branch of statistics that
provides techniques on how to model non-exact
relationships between two or more variables. For
example