Stat 350 - Assignment 2
Instructor: Jiguo Cao
It is due at 2:00pm Friday, June 15, 2012.
Please drop your assignment to the assignment-dropping box. It is
located right beside K9510, which is one level down the main oce
of Department of Statistics. Please
Stat 350 - Assignment 3
Instructor: Jiguo Cao
It is due at 2:00pm Friday, June 29, 2012.
Please drop your assignment to the assignment-dropping box. It is
located right beside K9510, which is one level down the main oce
of Department of Statistics. Please
Chapter 8
Indicator Variables
Linear Regression Analysis 5E
Montgomery, Peck & Vining
1
8.1 The General Concept of Indicator Variables
Qualitative variables also known as
categorical variables. Qualitative variables
do not have a scale of measurement.
I
Week 11
(Text Sections 19.2,23.1,23.2)
Example: Hospital stay data Let Yijk be the average length of stay in the k th hospital in region i with average age group j. We assume that the Yijk s are independent, and t the following model: Yijk N (ij , 2 ), wh
Week 2
(Text Chapter 1,2) Least-Squares Estimation (Ch.1) There are many dierent ways of estimating unknown parameters. One of the simplest is least-squares estimation. Denition: The least-squares estimators are the values 0 and 1 which minimize
n
S=
i=1
Week 10
(Text Sections 16.3) NOTE: On the midterm Q.3, there was a plot of the residuals vs. tted values. [INSERT PICTURE.] Many of you (incorrectly) said that there was a fan shape in this plot. When you assess such plots, keep in mind the number of poin
mea 1M 30/2062/1 [email protected]&
STAT 350 Assignment 3
Instructions: It is due at 5:00pm Tuesday, October 25., 2016. You do not need to
attach the R code for this assignment. Please show your calculation clearly.
Please drop your assignment to the assignment-d
STAT 350 Assignment 4
Instructions: It is due at 5:00pm Tuesday, November 1, 2016. Please show your calculation clearly. Make sure to answer each question in complete sentences and show your
calculation steps clearly.
Please drop your assignment to the as
STAT 350 Assignment 3
Instructions: It is due at 5:00pm Tuesday, October 25, 2016. You do not need to
attach the R code for this assignment. Please show your calculation clearly.
Please drop your assignment to the assignment-dropping box. It is located ri
Stat 350 - Assignment 1
Instructor: Jiguo Cao
It is due at 5:00pm Tuesday, October 4, 2016.
Please drop your assignment to the assignment-dropping box. It is
located right beside K9510, which is one level down the main office
of Department of Statistics.
Week 4
(Text Chapter 2) A CI gives us a range of plausible values for an unknown parameter. HTs allow us to test whether a parameter equals a specied value. Both depend on correct specication of the model! Steps for conducting a HT: 1. Identify your quest
Week 7
(Text Chapters 8.3, 8.4, 16) Types of Predictor Variables Predictor variables are either numeric or categorical. Numeric variables take on meaningful numeric quantities. They are further classied as continuous or discrete. Continuous variables can
Chapter 10
Variable Selection and
Model Building
Linear Regression Analysis 5E
Montgomery, Peck & Vining
1
10.1
Introduction
10.1.1 Model-Building Problem
Two conflicting goals in regression model building:
1. Want as many regressors as possible so that t
Statistics 350, Assignment 1
2015-09-16
This assignment is due, via the drop box outside K9510, by 11:30am on Tuesday
September 29 (no late submissions accepted). Collaboration is welcome, but you must
submit individual assignments, written in your own wo
Week 5
(Text Chapters 5, 6) Multiple Linear Regression (Ch.6) Normally we have more than one predictor. E.g., in the real estate data set, our original goal was to predict the selling price of a new house given the values of several predictor variables. D
Week 9
(Text Sections 2.9) R2 Denition: The coecient of determination, or R2 value, is dened as R2 = SSR SST O
Since SSR + SSE = SST O and all SS 0,SSR SST O 0 R2 1. Interpretation: R2 is the proportion of total variation in the response that is explained
Week 8
(Text Sections 2.7, 2.8, 7.1)
Sums of Squares Recall:
n n n
(Yi - Y )2 =
i=1 i=1
^ (Yi - Yi )2 +
i=1
^ (Yi - Y )2
SST O = SSE + SSR NOTE: SSE is actually the SS of the residuals, not the errors (the i 's), which are unknown. Idea: Partition the ob
Week 3
(Text Chapter 3) Checking Assumption #4: Plot of the Residuals vs. Order It's hard to check the independence assumption! One thing we can do is to plot the ri 's vs. the order in which they were collected (if this information exists). Such plots sh
Week 6
(Text Chapter 7) Multicollinearity (7.6) Multicollinearity is correlation among the regression coecient estimates (the j s). Typically, such correlation arises because of correlation among the predictor variables. E.g., family income, family saving
STAT 350 Assignment 5
Instructions: Instructions: It is due at 5:00pm Tuesday, November 15, 2016. Please
show your calculation clearly. Make sure to answer each question in complete sentences
and show your calculation steps clearly.
Please drop your assig
Stat 350 - Assignment 2
Instructor: Jiguo Cao
October 5, 2016
It is due at 5pm, Tuesday, October 11, 2016.
Questions
Consider the multiple linear model y = X + , where N ormal(0, 2 I)
1. Derive the least squares estimation for
2. Show that Cov(b
y) = 2 H
1.
Vehicle mileage vs emissions.
1.
Plot the
data.
2.
Consider the following 4 models for the data:
Two straight lines, one for each vehicle, with different
slopes and intercepts,
2.1.
2.2.
Two parallel straight lines.
2.3.
Two lines with the same interce
1.
When a weight is hung from a wire, the wire stretches (returning to its original
length when the weight is removed). A 1 kilogram weight is hung from a piece
of wire and the length stretched is measured. This is repeated and the two
resulting lengths a
1.
When a spring is stretched by an amount dfrom its original length a standard
theory predicts that the amount of work done will be K d2. In order to
estimate K, a spring is stretched by amounts of 0, 1, 2 and 3 units. For each of
these 4 values of d the