Chapter 6
Diagnostics for Leverage
and Influence
Regression Analysis 4e Montgomery,
Peck and Vining
1
6.1 Importance of Detecting Influential
Observations
Leverage Point:
unusual x-value;
very little effect
on regression
coefficients.
Regression Analys
MATH 338
Homework #5 SOLUTION
6.7
No observations show up as influential.
6.12
No observations show up as influential.
6.13
The last observation shows up as influential.
5.
1
() = ( )1 +
1
1
( ) ( )
1
1
() = ( )1 +
1
()
( )1 ( )1
1
2
= +
=
1 1
1
1
Introduction
In the area of applied statistics, a substantial portion of the analyses comes under the heading of linear models. This general heading
covers the major areas of regression analysis and the analysis of variance but includes other topics suc
Time Domain Models
Box & Jenkins popularized an approach to time series analysis
based on
Auto-Regressive
Integrated
Moving Average
(ARIMA) models.
1
Autoregressive Models
Autoregressive model of order p (AR(p):
xt = 1xt1 + 2xt2 + + pxtp + wt,
where:
Math 338/ Stat 438
Text:
Linear Model in Statistics
Spring, 2014
1. Main: Introduction to Linear Regression Analysis by D. C. Montgomery, E. A. Peck, and G. G. Vinning,
4th Edition, Wiley.
2. Reference:
(a) Introduction to Time Series Analysis and Forecas
1. a. From this correlation matrix we can see that multicollinearity may exist.
b. The variance inflation factors are the diagonal elements, which are 22051.96, 156211.21,
27348.36 and 173701.3.
c. The four eigenvalues are 2.24, 1.58, 0.19 and 0.0016.
d.
10.10
a. b. This subset model has four regressors: PRECIP, EDUC, NONWHITE and SO2.
For this subset model,
is 4.6394,
, and
c. Stepwise regression:
This model is the same as the one in part a and b.
10.14
a. The first subset model has three regressors: Fla
Characteristics of Time Series
A time series is a collection of observations made at dierent
times on a given system.
For example:
Earnings per share of Johnson and Johnson stock (quarterly);
Global temperature anomalies from 1856 1997 (annual);
Inve
NIath 338/438 NIid-term 1 Spring, 2014
NANIE: lKEY
o In each of the following problems always Show your work. Otherwise you will not
get full credit.
Problem Points
Total l. (12 points: 3 points for each correct identication) Answer
Math 338/ Stat 438
Homework 9
(Due: 25th April, Friday in class)
Spring, 2014
We strongly encourage students to form study groups. Students may discuss and work on homework
problems in groups. However, each student must write down the solutions independen
Math 338/ Stat 438
Homework 8
(Due: 18th April, Friday in class)
Spring, 2014
We strongly encourage students to form study groups. Students may discuss and work on homework
problems in groups. However, each student must write down the solutions independen
Math 338/ Stat 438
Homework 7
(Due: 11th April, Friday in class)
Spring, 2014
We strongly encourage students to form study groups. Students may discuss and work on homework
problems in groups. However, each student must write down the solutions independen
Chapter 5
Transformations and Weighting to
Correct Model Inadequacies
Regression Analysis 4e Montgomery,
Peck & Vining
1
5.1 Introduction
Regression Analysis 4e Montgomery,
Peck & Vining
2
5.1 Introduction
Data Transformation
Subject-Matter Knowledge
W
Chapter 2
Simple Linear Regression
Regression Analysis 4e Montgomery,
Peck & Vining
1
2.1 Simple Linear Regression Model
Single regressor, x; response, y
y = 0 + 1x +
Population
regression model
0 intercept: if x = 0 is in the range, then 0 is
the mean
Chapter 7
Polynomial Regression Models
Regression Analysis 4e Montgomery,
Peck & Vining
1
7.1 Introduction
A second-order polynomial in one variable:
y = 0 + 1 x + 2 x 2 +
A second-order polynomial in two variables:
y = 0 + 1 x1 + 2 x2 + x + 22 x + 12 x1
Chapter 4
Model Adequacy Checking
Regression Analysis 4e Montgomery,
Peck & Vining
1
4.1 Introduction
Assumptions
1. Relationship between response and regressors
is linear (at least approximately).
2. Error term, has zero mean
3. Error term, has constant
Chapter 3
Multiple Linear Regression
Regression Analysis 4e Montgomery,
Peck & Vining
1
3.1 Multiple Regression Models
Suppose that the yield in pounds of
conversion in a chemical process depends on
temperature and the catalyst concentration. A
multiple
Math 338/ Stat 438
Warm-up Exercises
Spring, 2011
1. Suppose we have a normal distribution with = 80, = 5 then
a. Calculate the z-score for a score of 90.
b. Find the percent of scores below 92.
c. Find the percent of scores greater than 87.
d. What score
Math 338/ Stat 438
Homework 1
Homework 1 (Due: 31st January, Friday in class)
Spring, 2014
For all students:
1. Problem 2.25 from the textbook.
2. Problem 2.26 from the textbook. (Hint: Assume errors to be normally distributed with zero
mean and constant
Chapter 15
Other Topics in the Use of
Regression Analysis
Regression Analysis 4E
Montgomery, Peck & Vining
1
15.1 Regression Models with
Autocorrelated Errors
15.1.1 Sources and Effects of Autocorrelation
Some applications of regression involve regressor