STATISTICS 608 Linear Models -EXAM I
February 19, 2015
Students Name:
Students Email Address:
INSTRUCTIONS FOR STUDENTS:
1. There are 9 pages including this cover page.
2. You have exactly 75 minutes to complete the exam.
3. There may be more than one cor
+
Stat 608 Chapter 3
+ Introduction: Checking
Assumptions
+
3
Summary
Chapter 2:
Set up model:
Inferences about model parameters & regression line
Dummy (categorical) variable regression
Chapter 3:
Check the model assumptions: Linear, Independent, Normal,
+
Chapter 8
Logistic Regression
1
+
Introduction and Setup
2
+
Linear Models?
Recall:
a linear model is one that can be written in matrix form as
That is, we can express y as a linear combination of the parameters
and the error term.
Models with transform
+
Stat 608 Chapter 2 (and 5)
Simple Linear regression
+ Introduction: Simple Linear
Regression Models
+
Simple Linear Regression (SLR) Models
We always draw a scatterplot first to obtain an idea of the
strength (measured by correlation), form (e.g., linea
+
Stat 608 Chapter 5
+
Multiple Linear Regression
Chapter
Multiple predictor variables
ANOVA and ANCOVA
Polynomial Regression
Assumption that model is valid
Chapter
6:
Leverage points
Transformations
Relationships between explanatory variables:
Multico
+
Stat 608 Chapter 7
Variable Selection
+
Introduction
Problems with multicollinearity:
Even when the model is significant, its possible that no individual
predictors are significant.
Slopes may have the wrong sign.
Predictors that explain substantial
+
Stat 608 Chapter 1
+
Theme of The Class
It makes
sense to base inferences or conclusions only on
valid models.
A
key step in any regression model, then, is to identify
and address model weaknesses.
There
are two main parts of the class:
1.
Choose appr
STATISTICS 608
Examination 2 Summer 2016
Duration: 120 MINUTES
Total points available: 40 (36 points = 100%)
SHOW ALL CALCULATIONS AND EXPLANATIONS. PARTIAL CREDIT
WILL ACCRUE FOR ALL RELEVANT WORK SHOWN.
YOU ARE NOT REQUIRED TO SHOW ANY R OR SAS CODE.
Th
Homework 3
1. State the geometric reason that for a dummy variable model with a single dummy
variable (i.e. yi = 0 + 1 xi + ei , where xi = 1 if success, 0 if failure)
that the
Psuch
5
first 5 observations are successes and the last 5 are failures (n = 10
Homework 7 (Written Section)
1. In a one-way ANOVA model with k = 3 groups and 4 observations per group:
(a) Use the F-statistic in Model Reduction Method 2 to derive a statistic for testing
whether the average of the means of the first two groups is the
+
Chapter 9
Serially Correlated Errors
+
Serially Correlated Errors
Data are often collected over time.
Our assumption so far has been 0 correlation among the errors.
Now we use Generalized Least Squares to fit models with
autocorrelated errors.
+
What is
+
Stat 608 Chapter 4
+
Weighted Least Squares
In Chapter 3, we saw that it is sometimes possible to overcome
nonconstant error variance by transforming Y and/or X . In this
chapter we consider an alternative way of coping with nonconstant
error variance,
Homework 8 (Written Section)
1. Suppose we are interested in the linear model yi = 0 + 1 x1i + 2 x2i + ei . Also suppose
the columns x1 and x2 of the design matrix for this model have mean 0 and length 1.
(That is, x01 x1 = 1, and the same is true of x2 .
Homework 5 (Written Section)
1. Suppose that for the model yi = + ei , the errors are independent with mean 0. Also
suppose that measurements are taken using one device for the first n1 measurements,
and then a more precise instrument was used for the nex
Homework 1
Instructions: On this and all homeworks and exams, please be sure your file has a cover page with
your name, email address, course and section number, and homework or exam number typed.
I. Matrix Algebra Review.
Define matrices A, B, and C as f
Homework 4
1. Explain in words why when we create confidence intervals and prediction intervals using
a transformed response variable Y we cant simply take the inverse transformation of
the endpoints to get a confidence or prediction interval in the origi
Homework 2: Written Section
1. Show that V ar (Yi ) = V ar (ei ) in the simple linear regression model. (Yes, this should
be that simple.) What did you assume?
2. Define in words only the least squares criterion.
3. Prove that Cov(aX, bY ) = ab Cov(X, Y )
Homework 6 (Written Section)
1. Cook and Weisberg (1999) describe an experiment with turkey growth. Methionine is
an amino acid essential for normal growth in turkeys; if they have too little, the birds
can be malnourished, but if they have too much, it c
STATISTICS 608 - Sample Examination 1
Duration: 75 MINUTES
Total points available: 22 (20 points =100%)
EXCEPT IN QUESTION 1, SHOW ALL CALCULATIONS AND EXPLANATIONS. PARTIAL
CREDIT WILL ACCRUE FOR ALL RELEVANT WORK SHOWN.
This paper consists of seven (7)
+
Stat 608
BLUE Notes
+
BLUE: Best Linear Unbiased Estimator
The Gauss-Markov Theorem says that our parameter estimate vector
is BLUE:
Best: Minimum Variance
Linear: A linear combination of Ys (we can write
Unbiased: That is,
Estimator: A statistic
as ay
COVER PAGE
STAT 608 Homework 04, Summer 2017
Please TYPE your name and email address
below, then convert to PDF and attach as the
first page of your homework upload.
NAME:
EMAIL:
STATISTICS 608
Homework 608 S17 04
Due: 11:59 PM, July 3, 2017
Question 1 [2
+
Stat 608 Chapter 5
+
Note to self
Add HW question on alternative hypothesis for model reduction
Add discussion on familywise error rate under model reduction
section
2
+
Multiple Linear Regression
Chapter
Multiple predictor variables
ANOVA and ANCOVA
P
+
Stat 608 Chapter 1
+
Theme of The Class
It makes
sense to base inferences or conclusions only on
valid models.
A
key step in any regression model, then, is to identify
and address model weaknesses.
There
are two main parts of the class:
1.
Choose appr
+
Stat 608 Chapter 7
Variable Selection
+
Introduction
Overspecified model (or contains irrelevant predictors):
MSE: fewer degrees of freedom.
Standard errors for regression coefficients inflated.
Thus: larger p-values and wider confidence intervals.
Unde
+
Stat 608 Chapter 4
+
Weighted Least Squares
In Chapter 3, we saw that it is sometimes possible to overcome
nonconstant error variance by transforming Y and/or X . In this
chapter we consider an alternative way of coping with nonconstant
error variance,
+
Stat 608 Chapter 3
+
Introduction: Checking
Assumptions
+
3
Summary
Chapter 2:
Set up model:
Inferences about model parameters & regression line
Dummy (categorical) variable regression
Chapter 3:
Check the model assumptions: Linear, Independent, Normal,
+
Stat 608 Chapter 1
+
Theme of The Class
It makes sense
to base inferences or conclusions only on
valid models.
A key step in
any regression model, then, is to identify
and address model weaknesses.
There
1.
2.
are two main parts of the class:
Choose
Stat 608 Chapter 3
Anscombes Four Data Sets
Valid Model
is the mean structure correct
is the variance structure correct
SAS Example
Is SLR a vaild model for any of these
datasets?
Using Residuals
One way of checking whether a valid
simple linear regressio
COVER PAGE
STAT 608 Homework 05 Summer 2017
Please TYPE your name and email address
below, then convert to PDF and attach as the
first page of your homework upload.
NAME:
EMAIL:
HOMEWORK NUMBER:
STATISTICS 608
Homework 608 S17 05
Due: 11:59 PM, July 8, 20
COVER PAGE
STAT 608 Homework 02, Summer 2017
Please write your name and email address
below and attach as the first page of your
homework upload.
NAME:
EMAIL:
STATISTICS 608
Homework 608 S17 02
Due: 11:59 PM, June 7, 2017
Question 1 [1 mark]
A straight li
COVER PAGE
STAT 608 Homework 06 Summer 2017
Please TYPE your name and email address
below, then convert to PDF and attach as the
first page of your homework upload.
NAME:
EMAIL:
STATISTICS 608
Homework 608 S17 06
Due: 11:59 PM, July 17, 2017
Question 1 [4
COVER PAGE
STAT 608 Homework 07 Summer 2017
Please TYPE your name and email address
below, then convert to PDF and attach as the
first page of your homework upload.
NAME:
EMAIL:
STATISTICS 608
Homework 608 S17 07
Due: 11:59 PM, July 20, 2017
Question 1 [1
STATISTICS 608
Homework 608 S17 01
Due: 11:59 PM, May 31, 2017
Question 1 [2+2+2=6 Marks]
A random variable X is normally distributed with mean
2
> 0.
and variance
(i) Find the density function of the random variable exp(X) and show a plot
of it. (Note: e