Stat 608 Chapter 2
Simple Linear regression
Simple Linear Regression
Models
A scatter plot of the data like that given in
Figure 2.1 should ALWAYS be drawn to
obtain an idea of the sort of relationship that
exists between two variables (e.g., linear,
quad
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
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 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 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
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
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 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 .
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Stat 608 Chapter 4
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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 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
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
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
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Stat 608 Chapter 1
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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
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Stat 608 Chapter 7
Variable Selection
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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
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Stat 608 Chapter 5
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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
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Stat 608 Chapter 2 (and 5)
Simple Linear regression
+ Introduction: Simple Linear
Regression Models
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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
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Chapter 8
Logistic Regression
1
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Introduction and Setup
2
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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
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Stat 608 Chapter 3
+ Introduction: Checking
Assumptions
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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,
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Chapter 9
Serially Correlated Errors
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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.
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What is