STAT GU4205/5205 Homework 2 [100 pts]
Due 6:10 pm Thursday, October 6th
Problem 1 (2.7 KNN) [35 pts]
Sixteen batches of plastic were made, and from each batch one test item was molded. Each
test item was randomly assigned to one of the four predetermined

GR5205
Linear regression
Handout 1
Due: Friday, Sep. 16 2016
Homework 1: Linear algebra
Before starting this homework, please study the notes that are posted at:
https:/sites.google.com/site/introlinearregression/NoteHW1.pdf
1. What is the rank of the n n

STAT GR5205: Homework 3 solutions
Maximum Possible Score: 100 Points
1. (5 points) Let 1 = [1, 1, 1] T . Then r f (1 ) = 1 Hence D1 f (1 ) = 1 T 1 = 3.
2. (a) (5 points) By definition of Directional derivative we know for small h that
f ( x0 + ha) f ( x0

GR5205
Linear regression
Handout 8
Due: Optional
Homework 8
1. Suppose that Yi =
P = X(X T X) 1 X T .
0
+
1 Xi1
+ . +
p Xip
iid
+ i , where i N (0,
2
) and define
(a) Prove that P 2 = P .
(b) Prove that T r(P ) = p + 1.
(c) Use part (a) to prove that 0 Pi

Outliers and influential cases
Statistics GR5205
Columbia University
Fall 2016
December 1, 2016
1
Outliers and influential cases
(Sections 10.210.4 in KNN)
True or False?
An outlier in a regression problem is a case with an unusual y-value.
2
False. Fix i

Weighted least squares
Statistics GR5205
Columbia University
Fall 2016
December 6, 2016
1
Final exam
Thursday, December 22, 9:00am to 12:00pm EST
You are allowed a calculator and two 8.5 by 11 sheets (4 sides
total) of original handwritten notes.
The exam

Linear Regression Models
Statistics 4205/5205 Spring 2017
Assignments
All homework problems are from Weisbergs Applied Linear Regression, fourth edition.
Homework 1: The following problems are due in class on Tuesday, January 31. You can
also submit your

Statistics 4205/5205, Fall 2016: Simple Linear Regression
Example: Forbes
This example concerns an experiment conducted by the Scottish physicist James D. Forbes in 1857,
concerning the relationship between atmospheric pressure and the boiling point of wa

Linear Regression Models
Statistics 4205/5205 Spring 2017
Assignments
All homework problems are from Weisbergs Applied Linear Regression, fourth edition.
Homework 1: The following problems are due in class on Tuesday, January 31. You can
also submit your

Linear Regression Models
Statistics 4205/5205 Spring 2017
Assignments
All homework problems are from Weisbergs Applied Linear Regression, fourth edition.
Homework 1: The following problems are due in class on Tuesday, January 31. You can
also submit your

Curvature and nonconstant variance
Statistics GR5205
Columbia University
Fall 2016
November 29, 2016
1
Announcements
1. Homework 7 is due Thursday, December 1.
2. Last day of class is Thursday, December 8.
3. Homework 8 will be due on Tuesday, December 13

The Simple Linear Regression Model
Statistics GR5205
Columbia University
Fall 2016
September 15, 2016
1
The simple linear regression model
Suppose our data consist of (X1, Y1), (X2, Y2), . . . , (Xn, Yn).
Under the simple linear regression (SLR) model, th

Introduction to Regression
Statistics GR5205
Columbia University
Fall 2016
September 13, 2016
1
Welcome!
Instructor:
Ron Neath, [email protected]
Office hours: Tue & Thu 10am11am, Friday 8:459:45, on
10th floor of SSW
Teaching assistant:
Guanhua Fan

Assignment 8 Solutions
1. (a) P2 = X ( X T X )1 X T X ( X T X )1 X T = X ( X T X )1 X T = P.
(b) tr ( P) = tr ( X ( X T X )1 X T ) = tr ( X T X )1 X T X ) = tr ( I p+1 ) = p + 1.
(c) Observe that P is symmetric. Hence, from 1.( a), we have Pii = nj=1 Pjj2

G5205 Linear Regression
Lecture 6 - 10/20/2016
Confidence intervals
Lecturer: Arian Maleki
Scribe: Arian Maleki
Summary
In Lecture 5, I summarized the three important questions that we would like to address in this course. These
questions are:
1. Does OLS

STAT GU4205/5205 Homework 1 [100 pts]
Due 6:10 am Thursday, September 22nd
Problem 1 (1.22 KNN) [20 pts]
Sixteen batches of the plastic were made, and from each batch one test item was molded.
Each test item was randomly assigned to one of the four predet

STAT GU4205/5205 Homework 3 [100 pts]
Due 6:10 pm Thursday, October 20th
Problem 1 [15 pts]
Consider the model
Yi = + i
iid
i N (0, 2 ).
i = 1, 2, . . . , n
The sample mean and sample variance are defined respectively as
n
1X
Yi
Y =
n i=1
and
n
SY2 =
1 X

STAT GU4205/5205 Homework 4 [100 pts]
Due 6:10pm Tuesday, November 22nd
Problem 1
The Tri-City Office Equipment Corporation sells an imported copier on a franchise basis
and performs preventive maintenance and repair service on this copier. The data have

STAT GU4205/5205 Homework 1 [100 pts]
Due 6:10 am Thursday, September 22nd
Problem 1 (1.22 KNN)
Sixteen batches of the plastic were made, and from each batch one test item was molded.
Each test item was randomly assigned to one of the four predetermined t

Linear regression in action
Arian Maleki
Example 1: Should I buy a house in US?
For the reasons I will mention later the answer we give to this
question will not be satisfying. But it is a nice example and will help
you learn the topic. Also, the appro

Lecture 8 - 11/10/2016
G5205 Linear Regression
Bias-variance trade-off and cross-validation
Lecturer: Arian Maleki
1
Scribe: Arian Maleki
What is next?
So far we have only considered linear models. Linear models are quite useful for applications. However,

G5205 Linear Regression
Lecture 6 - 10/15/2016
Maximum likelihood interpretation of OLS and its implications
Lecturer: Arian Maleki
Scribe: Arian Maleki
Summary
In the last lecture we raised three questions that we would like to address. These questions w

Lecture 1 - 9/12/2016
G5205 Intro to Linear Regression
Review of Calculus
Lecturer: Arian Maleki
Scribe: Arian Maleki
One of the main tools used in this course is calculus. Concepts like derivative, local maxima and minima,
second derivative, mean value t

G5205 Linear Regression
Lecture 11 - 12/8/2016
Multicolinearity and outlier detection
Lecturer: Arian Maleki
Scribe: Arian Maleki
In addition to all the issues that I mentioned in the last lecture, there are two more issues that we may
face in practice: m

G5205 Linear Regression
Lecture 3 - 9/22/2016
Ordinary Least Squares Formulation
Lecturer: Arian Maleki
1
Scribe: Arian Maleki
Least square for the univariate case (simple linear regression)
Consider the education example we discussed in our first lecture

How to use linear regression in practice?
Arian Maleki
Department of Statistics, Columbia University
1 / 19
Dataset 1: Final Exam Dataset
Dataset:
I
I
I
I
House prices in several neighborhoods of Seattle.
Several features of these houses are given.
More t

Lecture 5 - 10/5/2016
G5205 Linear Regression
Gaussian random vectors and maximum likelihood
Lecturer: Arian Maleki
Scribe: Arian Maleki
Motivation
So far we have studied the linear regression model. In linear regression, the observations are assumed to
s

Lecture 9 - 12/1/2016
G5205 Linear Regression
How to detect and resolve high-bias and high-variance issues?
Lecturer: Arian Maleki
Scribe: Arian Maleki
As we discussed in the last section there are two main problems a linear regression model can suffer fr

Linear Regression Models
Statistics GR5205 Fall 2016
Section 005: TR 8:40pm9:55am; 903 SSW
Instructor:
Ronald Neath
[email protected]
Office hours:
Time and location to be announced
Course description: This is a first course in regression analysis for