Linear Regression Models
Statistics W4315 Fall 2015
Assignment 1
Reading:
By Friday, September 11, read Appendix A and Chapter 1 of Applied Linear Regression Models by
Kutner, Nachtsheim and Neter (KNN).
For September 18, read Sections 2.12.5 of KNN.
For
Homework 3
STAT W4315: Linear Regression Models
Simple Linear Regression Model
DUE: Monday, October, 19, 12:00 noon
(1) Please sign your home work with your name and UNI number.
(2) Homework must be submitted into the Statistics Homework Boxes room 904 on
Linear Regression Models
Statistics W4315 Fall 2015
Assignment 2
Reading:
By Thursday, September 17, read Appendix A and Chapters 12 of Applied Linear Regression
Models by Kutner, Nachtsheim and Neter (KNN).
For Thursday, September 24, read Chapter 3 of K
Linear Regression Models
Statistics W4315 Fall 2015
Assignment 1
Reading:
By Thursday, September 10, read Appendix A and Chapter 1 of Applied Linear Regression Models
by Kutner, Nachtsheim and Neter (KNN).
For Thursday, September 17, read Chapter 2 of KNN
Homework 1 (with solutions)
STAT W4315: Linear Regression Models
Simple Linear Regression Model
DUE: Wednesday, September, 23, 12:00 noon
(1) Please sign your home work with your name and UNI number.
(2) Homework must be submitted into the Statistics Home
Homework 3 (with solutions)
STAT W4315: Linear Regression Models
Simple Linear Regression Model
DUE: Monday, October, 19, 12:00 noon
(1) Please sign your home work with your name and UNI number.
(2) Homework must be submitted into the Statistics Homework
Linear Regression Models
Statistics W4315 Fall 2015
Assignment 1
Reading:
By Thursday, September 10, read Appendix A and Chapter 1 of Applied Linear Regression Models
by Kutner, Nachtsheim and Neter (KNN).
For Thursday, September 17, read Chapter 2 of KNN
Homework 3 Solutions, Stat 4315, Fall 2009 Problems: 3.19, 3.20, 3.24, 4.10, 4.21, 4.25, 5.23, 5.29, 5.30
Problem 3.19 The plot against the fitted values is preferable. If there isn't a relationship between e_i and the fitted values it implies there isn't
Linear Regression Models
Statistics W4315 Fall 2015
Assignment 2
Reading:
By Friday, September 18, read Appendix A and Chapters 12 of Applied Linear Regression Models
by Kutner, Nachtsheim and Neter (KNN).
For Friday, September 25, read Chapter 3 of KNN.
Diagnostics and Remedial Measures
Yang Feng
http:/www.stat.columbia.edu/~yangfeng
Yang Feng (Columbia University)
Diagnostics and Remedial Measures
http:/www.stat.columbia.edu/~yangfeng
/ 76
Remedial Measures
How do we know that the regression function is
Linear Regression Models SAS Homework 6 14.9 a) Maximum likelihood estimate of 0: -10.3089 Maximum likelihood estimate of 1: 0.0189 Fitted response function: phat = exp(-10.3089+0.0189X)/(1+exp(-10.3089+0.0189X) b) The fitted logistic response function ap
Student Solutions Manual to accompany Applied Linear Regression Models Fourth Edition
Michael H. Kutner Emory University Christopher J. Nachtsheim University of Minnesota John Neter University of Georgia
2004 McGraw-Hill/Irwin Chicago, IL Boston, MA
PREFA
Part
Simple Linear Regression
I
Chapter
1
Linear Regression with One Predictor Variable
Regression analysis is a statistical methodology that utilizes the relation between two or more quantitative variables so that a response or outcome variable can be pr
Solutions to Homework 2, Stat 4315, Fall 2009
2.3 Two points, 1) Look at the p-value is there evidence that the slope is significantly different than zero? What does that say about the interpretation of the statement given? 2) Who plays interactive market
Chapter
2
Yi = 0 + 1 X i + i (2.1)
Inferences in Regression and Correlation Analysis
In this chapter, we first take up inferences concerning the regression parameters 0 and 1 , considering both interval estimation of these parameters and tests about them.
Matrix approach to simple linear regression
Statistics W4315
Columbia University
Fall 2015
October 16, 2015
1
Quick review of matrix algebra (Sections 5.15.6)
Matrix addition.
Add the terms elementwise.
Let A = (aij ) and B = (bij ) be matrices w same di
Diagnostics
Statistics W4315
Columbia University
Fall 2015
September 25, 2015
1
Course stu
Homework 1 is due today!
Submit your paper by 12noon (NYC time) on Monday!
Section 003: submit paper copy to mailbox in Room 904 SSW.
Section D04: submit pdf throug
The Simple Linear Regression Model
Statistics W4315
Columbia University
Fall 2015
September 18, 2015
1
The simple linear regression model
Suppose our data consist of (X1, Y1), (X2, Y2), . . . , (Xn, Yn).
Under the simple linear regression (SLR) model, the
Multiple Regression
Yang Feng
Yang Feng (Columbia University)
Multiple Regression
1 / 41
Multiple regression
One of the most widely used tools in statistical analysis
Matrix expressions for multiple regression are the same as for simple
linear regression
Introduction to Regression
Statistics W4315
Columbia University
Fall 2015
September 11, 2015
1
Welcome!
Instructor:
Ron Neath, rcn2112@columbia.edu
O
ce hours: Friday 1:303:00pm, 10th oor of SSW
Teaching assistant:
Yuanjun Gao, yg2312@columbia.edu
O
c
Prediction intervals; the analysis of variance
Statistics W4315
Columbia University
Fall 2015
September 25, 2015
1
Review (Sec 2.4)
Let xh denote a xed x-value
A point estimate of
E(Y |X = xh)
is
b 0 + b 1 xh = Y h
How about a 1
condence interval for
0 +
Testing for lack of t
Statistics W4315
Columbia University
Fall 2015
October 2, 2015
1
Announcements
1. Instructors Friday o
ce hour:
1:303:00pm 10th oor SSW 1:002:30pm 703 Hamilton
2. Homework 2 is due today!
October 5.
Submit by noon on Monday,
3. Homew
Inference in Simple Linear Regression
Statistics W4315
Columbia University
Fall 2015
September 18, 2015
1
The Simple Linear Regression Model
Let x1, x2, . . . , xn be xed values.
(If they are realizations of a random variable then all inference
is conditi
Testing for lack of t
Statistics W4315
Columbia University
Fall 2015
October 2, 2015
1
Announcements
1. Instructors Friday o
ce hour:
1:303:00pm 10th oor SSW 1:002:30pm 703 Hamilton
2. Homework 2 is due today!
October 5.
Submit by noon on Monday,
3. Homew
Transformations in simple linear regression
Statistics W4315
Columbia University
Fall 2015
October 2, 2015
1
Remedial measures: transformations (Secs 3.83.9)
Example: Let
X = tree diameter in mm
Y = tree height in decimeters
Data: (xi, yi) for i = 1, 2, .
Categorical predictor variables
Statistics W4315
Columbia University
Fall 2015
November 13, 2015
1
Qualitative Predictors (Sec 8.3)
Example 1: Small-scale experimental study of the relation of
brand preference to moisture and sweetness of the product
Resp
Multicollinearity
Statistics W4315
Columbia University
Fall 2015
November 13, 2015
1
Introduction
Our data consist of n independent observations from the joint
distribution of
(Y ; X1, X2, . . . , Xp 1)
Fitting the mean function
E[Y |X = x] = 0 + 1x1 + 2x
Linear Algebra Review
Yang Feng
Yang Feng (Columbia University)
Linear Algebra Review
1 / 46
Denition of Matrix
Rectangular array of elements arranged in rows and columns
16000 23
33000 47
21000 35
A matrix has dimensions
The dimension of a matrix is its
Bivariate normal distribution
Statistics W4315
Columbia University
Fall 2015
October 9, 2015
1
The bivariate normal distribution (Sec. 2.11)
The random variables (X, Y ) have a bivariate normal distribution
if their joint density function is
q
f (x, y) =
# Read in the ozone data
# (You'll probably have to change this part.)
getwd()
Data <- read.table("ozone.txt", header=T)
names(Data)
x <- Data$Temperature
y <- Data$Ozone
# Regression of Ozone concentration on temperature
m1 <- lm(y ~ x)
plot(y ~ x) ; l
Inference in Simple Linear Regression
Statistics GR5205
Columbia University
Fall 2016
September 20, 2016
1
The Simple Linear Regression Model
Let x1, x2, . . . , xn be fixed values.
(If they are realizations of a random variable then all inference
is cond