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(0, 2 ). Let b0 and b1 be the estimators of 0 and 1 resp
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 linear regression model that might describe this
relationshi
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 formaldehyde concentration(CH2 O) inside the house.
Twelve homes
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 this model can be written as
yi = 0 + 1 xi + , i = 1, 2,
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 occasionally useful.
Suppose we re-dene the regression variable
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
Regression modeling leads to a mathematical description of
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).
The simple regression model is
y = + = 0 + 1 x +
whe
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 explanatory
variable. We can also refer it as the tted v
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
coecients(t) # model coecients
connt(t, level=0.95) # CIs
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 and a specic model (with a set of
assumptions), least-
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 (xi x )2 .
i=1
The constant ci has several properties:
n
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, medical scientists involved in research on
the eye ar