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 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 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
Lecture 8-2
Sampling Distributions
Sampling Distributions
Statistics can be viewed as random variables
from a probability distribution.
Suppose we draw multiple samples from a
population.
Each sample contains different observations.
Consequence: Value
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 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 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
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 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 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 1-5
Descriptive Statistics:
Variability or Dispersion
1
Measures of Variability/Dispersion
Measures of central tendency give information
only about the typical value.
Real data exhibit variability.
2
Common Measures of Variability
Sample Range
Lecture 1-6
Descriptive Statistics:
Data Displays
1
Important Data Displays
Stem-and-Leaf Plots
Histograms
Boxplots
Time Plots
Normal Probabiltiy Plots
Q-Q Plots
2
Stem-and-Leaf Plot
Displays the shape of the data
Only loss of information: time order
U
Lecture 1-4
Descriptive Statistics
Central Tendency
1
Descriptive Statistics
Two important characteristics of a population
Center: measures of central tendency
Behavior around the center: measures of
variability or dispersion
Examples of central tende
STAT 4706
Exam # 1 Formula Sheet
Fall 2013
If there are n observations in a sample, denoted x1,x2,xn, the sample mean and variance are expressed as
n
n
1
x
= xi
n i=1
n
n
1
S=
x
( x )2
n1 i=1 i
2
2
x
S = i=1
2
i
( )
i=1
x
and s 2 .
2
xi
n
n1
If there a
Estimating Proportions
9.10 Single Sample: Estimating a proportion
9.11 Two Samples: Estimating the difference Between
Two proportions
9.12-9.14 Will not be covered.
1
Overview
A sample of size n is taken, and the number of
observations in a sample label
23,2k Factorial and Fractional
Factorial Experiments
1
Lecture 15-4
Fractional Factorial Design
2
Even for a moderate number of factors,
the 2k factorial can require an excessive
number of runs.
A possible solution: Fractional Factorial
Designs.
First,
STAT-4706
Homework # 5 Solutions
1. 11.2 pg. 398
2. 11.6 pg. 399
3. 11.16 pg. 411
1
Fall 2014
STAT-4706
Homework # 5 Solutions
Fall 2014
n
S yyb 1 S xy
NOTE: S =MSE= n2
2
b1=
i=1
n
n
n
i=1
i=1
( )( )
( )
n xi yi
xi yi
n x 2
i
i=1
2
n
i=1
xi
=
S xy
S xx