STAT 410/510 F-2011 Midterm I
NAME: _
1. Consider the simple linear regression model
where the intercept
is known. (30 points
total)
a. Find the LS estimator of for this model. (9 points)
Answer)
( ) (
) where
is known. After taking the derivative of ( )
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 1: Overview of Regression Analysis
Regression analysis is a statistical tool for investigating relationships among variables.
Examples:
Home sale prices may depend on the location, size and yea
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 6
Using the Model for Estimation and Prediction
We will learn:
A confidence interval for estimating the mean response for a given value of the
predictor x
A prediction interval for predicting a
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 7
Diagnostics and Remedial Measures
What can go wrong with the model?
1)
2)
3)
4)
5)
6)
The regression model is not linear
The error variance is not constant
i are not independent
i are not dis
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 2
Simple Linear Regression
Suppose we have observations on subjects consisting of a dependent variable and an
explanatory variable .
Table 1: Data
Given the data set, n pairs of observations,
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 6
Measure the strength of linear association
Coefficient of determination
2 =
=1-
0 2 1
2 *100 percent of the variation in is explained by the variation in predictor
r is called the correlat
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 3
Simple Linear Regression
Maximum Likelihood Approach
Assume
then
Probability density function for :
Likelihood function for n observations, 1 , 2 , , :
Maximizing log likelihood function wi
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 4
Inference concerning
Hypothesis Test for 1
Test whether there is a linear association between x and y
Decision Rule
The confidence interval at the (1-)100% level for 1 is
.
Inference concer
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 8
Diagnostics and Remedial Measures (Continued)
Normality of Error Terms
Residuals that are normally distributed
Normal Probability Plot
Right Skew - If the plotted points appear to bend up and
STAT 475
Chapter 5 GETTING DATA INTO SAS
There are several ways to input data into SAS:
(1) Entering data directly into SAS code (called reading instream data).
(2) Creating dataset inside SAS code using the DO statement.
(3) Referencing a SAS data file s
F2011 STAT 410/510
Chapter 9 Building the regression model I: Model
selection and validation
Surgical Unit Example:
A hospital surgical unit was interested in predicting survival (Y) in
patients undergoing a particular type of liver operation. A random
se
F-2011 STAT 410/510
Chapter 6. Multiple Regression I
6.1 Multiple regression models:
First-order model with two predictor variables:
Yi 0 1 X i1 2 X i 2 i
Assuming that Ecfw_ i 0, Ecfw_Y 0 1 X1 2 X 2
Then, the regression function is a plane. See Figure
F-2011 STAT 510
Chapter 5 Matrix approach to simple linear regression
For linear model: y 0 1x
Y1 1 X1
1
Y 1 X
2 0 2
2
=
1 1
n
Yn 1 X n
Y1
Y
Let Yn1 2 be the vector of n observations on the response
Yn
variable and let
1 X 1
1 X
X n2 2
Chapter 4 Simultaneous inferences and other topics in
Regression analysis
4.1 Bonferroni joint CIs for 0 and
1
We will learn a procedure for constructing simultaneous CIs for 0
and 1 with a specified family confidence coefficient.
Note that the meaning of
F-2011 STAT 410/510 Midterm Exam 2
NAME: _
1. The following data is concerning the proportion of coal miners who exhibit symptoms of severe
pneumoconiosis and the number of years of exposure. The data are shown below:
Years of exposure
5.8
15.0
21.5
27.5
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 10
General Linear Model
Special Cases
Interaction Effect
Qualitative Predictor Variables
Example: Predict length of hospital stay (Y) based on age (X1) and gender
(X2) of the patient.
Polynomia