Using Linear Regression for
Model Building
Simple Linear Regression
1
Reading Assignment
Read Chapter 11
Section 11.1: Introduction to Linear Regression
Section 11.2: Simple Linear Regression (SLR)
Section 11.3-4: Least Squares & Fitted Model
Section
STAT-4706
Homework # 5
Summer 2013
You must show all of your work for each problem in order to receive full credit. Minitab should
be used when specified. HW is due 08/15/2013. MLR
1. The data in the excel file relief.xlsx represent the number of hours of
Using Linear Regression for
Model Building
Chapter 11
Scatterplots & Correlation
1
Reading Assignment
Read Chapter 11
Section 11.12: Correlation
2
Multivariate Data
In engineering studies involving multivariate
data, often the objective is to determine
STAT-4706
Homework # 1
Summer 2013
You must show all of your work for each problem in order to receive full credit. Minitab
should be used when specified. HW Due 07/12/2013.
1. (25) The reaction times, for a random sample of 9 subjects to a stimulant were
STAT-4706
Homework # 1 Solutions
Fall 2014
You must show all of your work for each problem in order to receive full credit. Minitab should be
used when specified. HW Due 09/11/2014.
1. (30) For the following sample whose observations, 15, 7, 8, 95, 19, 12
STAT-4706
Solutions Homework # 2
Fall 2014
You must show all of your work for each problem in order to receive full credit. HW Due
09/25/2014.
1. (16) A random sample of 12 graduates of a certain secretarial school typed an average
of 79.3 words per minut
STAT-4706
Solutions Homework # 3
Fall 2014
You must show all of your work for each problem in order to receive full credit. HW is due
09/02/2014.
1. (11) It is claimed that automobiles are driven on average more than 20,000 Km per year. To test
this claim
Lecture 9-3
Other Intervals for
Prediction Intervals
Confidence intervals provide good information
about the unknown parameter .
Prediction intervals, estimate the possible
value of a future observation.
Must account for
variation due to estimating th
Lecture 9-5
Confidence Intervals for
Paired Data
Motivation
Before and after.
See if there are changes in the subject.
Initial reading is given, an experiment is
performed, then a second reading is given.
Multiple measurements, different conditions.
Lecture 8-5
and F Distributions
- Distribution
The - Distribution describes the random
behavior of sample variances.
Simplest case involves , sample variance.
Assumptions
Random sample
Normal distribution
Very sensitive to the normality assumption!
Lecture 8-4
t Distribution
What If the Variance Is Unknown?
In real-life, the variance is rarely known.
What is a reasonable strategy?
2
What If the Variance Is Unknown?
Consider
X
s/ n
Important issue: What distribution does this
statistic follow?
3
Lecture 9-2
Confidence
Intervals for
Confidence Intervals, 2 Known
2
Confidence Intervals, Known
2
With some algebra:
)
Thus, our interval is
Note: is not random!
The limits are random!
3
Confidence Intervals, Known
2
For a specific interval, give
Lecture 8-3
Central Limit Theorem
Distributions of Sample Means
Much of classical statistical analysis uses
sample means.
Critical question: What is the distribution?
For normal population: sample means are normal
Rarely have data from a true normal d
22 Factorial Experiments
Section 15.2
1
Background
The 22 factorial design is an extension of
the two-sample t-test.
Two Factors: A and B
Each at two levels:
High or +1
Low or -1
Background
Let x1 be the design variable or coded
factor setting for F
Lecture 10-7
Hypothesis Tests for Proportions
Test for a Single Proportion
Recall that the following conditions for the
binomial to be approximated by the normal:
np > 5, n(1-p) > 5 (prefer 10).
Consider the null hypothesis
H0: p = p0.
Be careful not t
Lecture 10-4
Hypothesis Tests for a Single Mean,
Variance Unknown
Basics
Let X1, X2, , Xn is a random sample from a well
behaved distribution.
Estimate the population variance by the
sample variance, S2.
Consequence: use the t statistic
How will this
Lecture 10-5
Hypothesis Tests for Difference of
Two Means, Paired Data
Paired Data
Basic idea discussed in Chapter 9.
Classic example: Octane study
Take a set of gasoline blends
Split each blend into two batches
Measure octane using method A on one
Lecture 10-3
Hypothesis Tests for a Single Mean,
More on Power
Concept of Power
Power is the probability
We reject the nominal claim,
When the alternative claim, , is true
Power depends upon , the alternative!
Formal calculation of power requires a s
Lecture 10-5
Hypothesis Tests for Difference of
Two Means, Variances Unknown
Basics: Independent Samples
X 11 , X 12 ,., X 1n is a random sample of size n1
from population 1.
X 21, X 22 ,., X 2 n is a random sample of size n2
from population 2.
The two
Lecture 10-1
Overview of Hypothesis Tests
Basic Framework
The way we use data to answer questions about
parameters is very similar to how juries evaluate
evidence about a defendant.
We start with a nominal claim, which we call a null
hypothesis, H0.
H0:
Lecture 9-6
Confidence Intervals for Proportions
Basics
Recall the binomial distribution
is the number of successes
is the size of the random sample
is the probability of a success
Can approximate by normal if smaller of and
> 5 (prefer > 10)
2
Con.
Lecture 9-4
Confidence Intervals for
Difference of Two
Independent Means
Variances Known
is a random sample of size n1 from population
1.
is a random sample of size n2 from population
2.
The two populations are independent.
Knowledge of one: no inform
Lecture 9-1
Introduction to Estimation
Overview of Estimation
2
Estimators
An unbiased estimator of an unknown
parameter is one whose expected value is
equal to the parameter of interest.
Thus, we call an unbiased estimator of
if
E[ ]
Thus the estim
Lecture 8-1
Review of the Normal Distribution
Normal Distribution
Most widely used probability model.
Major reason: The Central Limit Theorem
Defined by two parameters
E(X) =
variance of V(X) = 2.
pdf:
f ( x)
1
e
2
x 2
2 2
for x .
Normal Distrib
INTRODUCTION TO
HYPOTHESIS TESTING
CHAPTER 10
10.1 Statistical Hypothesis: General Concepts.
10.2 Testing a Statistical Hypothesis.
10.3 P-values for Decision Making.
1
Overview of Testing
The way we use data to answer questions about
parameters is very
Stat-4706
Minitab Handout
Model Building
Model Building techniques in Minitab 17
Below are the steps to perform Model Selection using Minitab 17. The data for the problem is
the same data we used in class. This data can be found on Scholar under the resou
Stat 4706
Multiple Comparisons Minitab Example
You design an experiment to assess the durability of four experimental carpet products. You place a
sample of each of the carpet products in four homes and you measure durability after 60 days.
Because you wi
2k Factorial Experiments
Introduction
Chapter 15
1
Introduction
Designed experiments intentionally disturb
the process
Observe the results.
Example: Consider the yield
(concentration of desired product) from a
distillation column.
Response characteris
STAT-4706
ONE-WAY ANOVA Minitab Handout
Performing One-way ANOVA, Computing P-values
Performing ANOVA in Minitab 17
Below are the steps for ANOVA using Minitab 17. The data for the problem is the same data we
used in class. The data is in the excel file C
HYPOTHESIS TESTING FOR
ONE POPULATION MEAN
CHAPTER 10
10.4 Single Sample: Tests Concerning a single Mean.
Using CI for Hypothesis Testing
1
Hypothesis Testing About the Mean
Sigma () Known
We assume X1, X2, , Xn is a random
sample from a population with