NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
1.
ST3131 Regression Analysis
Tutorial 3
A regression model y = 0 + 1x1 + 2 x2 + was fitted to eleven observations. The
data were summarized as follows.
T
Chapter 7
Using Transformation in
Regression Models
ST3131 Regression Analysis
CYM
7-1
7.1 Introduction
Reasons for a transformation of data
• Transformation of data can sometimes reduce
complex models to linear ones.
•
Transforming a non-linear model in
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
ST3131 Regression Analysis
Tutorial 2
1. Eight runs were made at various conditions of saturation (x1) and transisomers (x2).
The response, SCI, is denote
Chapter 5
Testing a General Linear
Hypothesis
ST3131 Regression Analysis
CYM
5-1
5.1 Introduction
• Consider the model y = β0 + β1x1 + β2x2 + ε
• Suppose that we suspect β1 = β2, then a model
y = β0 + β1(x1 + x2) + ε
should be used.
• We want to test
H0:
Chapter 6
Polynomial Regression Models
ST3131 Regression Analysis
CYM
6-1
6.1 Introduction
• Relationships between variables are not always
linear.
• Sometimes we have nonlinear relationships
between variables.
• For example,
yi = β0 + β1x1i + β2x1i2 + ε
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
ST3131 Regression Analysis
Tutorial 1
1. The data given below were obtained from an experiment with 10 cars. The
amount of additive x and the amount of re
Chapter 4
Lack of Fit Test
ST3131 Regression Analysis
CYM
4-1
4.1 SS Pure Error and SS LOF
To test for the appropriateness of a particular
multiple regression model, we perform a lack of fit
test.
To test for lack of fit, at least two independent
measur
Chapter 3
Measuring association in the
multiple regression model
ST3131 Regression Analysis
CYM
3-1
3.1 Coefficient of Multiple Determination
• To measure the adequacy of a multiple regression
model, we use a measure called the coefficient of
multiple de
Chapter 2
Multiple Regression Model
ST3131 Regression Analysis
CYM
2-1
2.1 Multiple Regression Model
• A regression model that involves more than one
independent variables is called a multiple
regression model.
• The general form of a regression model wi
Chapter 8
Use of “Dummy” Variables
ST3131 Regression Analysis
CYM
8-1
8.1 Introduction
•
How to handle predictor variables which are
categorical?
•
Examples of categorical variables
1. Different types of fertilizers on the yield of rice.
2. Different tea
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
ST3131 Regression Analysis
Tutorial 4
1. Twenty observations were taken from the model y = 0 + 1x1 + 2 x2 + 3 x3 + .
The following matrices were then obta
Chapter 9
Selection of an Appropriate Model
ST3131 Regression Analysis
CYM
9-1
9.1 Introduction
Two opposed criteria of selecting a model are usually
involved:
1. To include as many predictor variables as possible
so that reliable fitted values can be ob
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
1.
ST3131 Regression Analysis
Tutorial 8
A professor wishes to compare three different teaching methods. She divides 30
students into three randomly assig
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
ST3131 Regression Analysis
Note: This tutorial will be discussed in the lecture on 9 April 2013
Tutorial 9
1.
Refer to Question 2 in Tutorial 8. Apply (a)
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
1.
ST3131 Regression Analysis
Tutorial 7
In an environmental engineering study of a certain chemical reaction, the
concentrations of 18 separately prepare
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
1.
ST3131 Regression Analysis
Tutorial 6
The effectiveness of a new experimental overdrive gear in reducing patrol consumption
was studied in 12 trials wi
NATIONAL UNIVERSITY OF SINGAPORE
Department of Statistics and Applied Probability
2012/13 Semester 2
1.
ST3131 Regression Analysis
Tutorial 5
The following data represent the heat evolved in calories per gram of cement (y) as a
function of the amount of e
Statistical Project for ST3131(2012/13 Semester 2)
Objective:
Apply regression analysis technique to analyze a real data set.
What to do:
1.
Formulating your own problem: Find a problem that regression analysis can be used. The
problem is to study how a s