Departures from Normality
Back to Binomial
Random Rectangles Activity
Sampling
Bias
The Binomial and Normal Distributions
Betsy Greenberg
Betsy Greenberg
Statistics and Modeling
McCombs
Departures from Normality
Back to Binomial
Random Rectangles Activity
QUESTION 13
For the following report about a statistical study, identify the items below.
A business magazine mailed a questionnaire to the treasurer of the top 500 profitable companies, and
received responses from 20% of them. Those responding reported t
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
CLASSICAL SEASONAL DECOMPOSITION - MULTIPLICATIVE MODELS
Examples of Seasonality
Quarterly sales for Wal-Mart for 33 quarters
8000
S 6000
a
l 4000
e
s
2000
Qtr 1
Qtr 1
Qtr
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
SEASONAL DECOMPOSITION FOR ADDITIVE MODELS USING
CLASSICAL, RATIO-TO-MOVING AVERAGE AND STL (R PACKAGE) METHODS
Two types of models are used for seasonal decomposition:
(1)
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
LAGGED Y-VALUES
Recall the deterministic model
At = exp( + 1t + 2t2 + t)
t iid N(0, 2).
To estimate , 1 and 2 we run the regression
log(At) = + 1t + 2t2 + t
t iid N(0, 2).
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Spring 2017
HOMEWORK #5 ANSWERS
1. The file STA372_Homework5_Question1.dat on the Data sets page of the Canvas class
website contains 40 quarters of sales data for The Gap (in thousand
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
RANDOM WALK MODELS
Data: 64 quarters (16 years) of the U.S. - Japanese Exchange Rate
Exchange Rate with Japan
280
210
140
70
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
Th
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Spring 2017
HOMEWORK #4 ANSWERS
1. The pharmaceutical industry in the U.S. and many other parts of the world has
experienced substantial growth, considerable restructuring, numerous me
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Spring 2017
INTRODUCTORY LECTURE
Example of trend and seasonal patterns
Data: 44 quarters of sales for The Gap
Quarterly sales for The Gap for 44 quarters
1600000
800000
Qtr 1
Qtr 1
Qt
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
DETERMINISTIC TREND FITTING - CONFIDENCE INTERVALS
Data: 85 quarters of Wal-Mart sales
Seasonal
Log
Quadratic
Exponential
Reseasonalize
Yt At
Wt
W t
At
Yt
Adjustment Trans
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Spring 2017
HOMEWORK #1 ANSWERS
1. The Excel spreadsheet STA372_Homework1_Question1.xlsx on the Data sets page of
the Canvas class website contains 33 quarters of quarterly sales data
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Spring 2017
HOMEWORK #3 ANSWERS
1. The pharmaceutical industry in the U.S. and many other parts of the world has
experienced substantial growth, considerable restructuring, numerous me
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
REGRESSION
The notes start on the next page.
1
True regression model
Sales vs. Time
15
True regression line
Sales = + Time
14
13
12
Sales
11
10
9
8
7
6
0
1
2
3
4
5
6
7
8
9
THE UNIVERSITY OF TEXAS AT AUSTIN
McCombs School of Business
STA 372.5
Tom Shively
ESTIMATING THE VARIANCE OF EPSILON
The notes start on the next page.
1
Relationship between and e
Sales vs. Time
15
True regression line
Sales = + Time
14
13
12
Sales
11
10
Linear Prediction
Last time we tried to find a relationship between our response variable X
and our explanatory variable Y .
Here, there appears to be a linear relationship between price and size:
STA 371g: Statistics and Modeling
200
200
150
150
Price
Pr
What have we covered?
I
STA 371g: Statistics and Modeling
Lecture 11: Midterm review
Discrete random variables:
I
Marginal, Conditional and Joint probabilities.
I
Expectation and Variance
I
The normal distribution.
I
Sampling from the normal distribution:
Including non-numerical variables
What factors influence house price?
STA 371g: Statistics and Modeling
Lecture 20: Dummy Variables and Interactions
Sinead Williamson
The University of Texas McCombs School of Business
I
Size
I
Number of bathrooms
I
Neighb
Sensitivity Analysis recap
Last week, we explored how we can use software to make evaluating
decision trees easier.
STA 371g: Statistics and Modeling
In particular, PrecisionTree makes it easier to run sensitivity analysis,
Lecture 8: More Complex Decisio
Recap
Last lecture, we looked at basic probabilities:
STA 371g: Statistics and Modeling
I
What is a probability? What is a random variable?
I
How can we combine the probability of independent events? If two
independent events A and B have probabilities P(
Simple linear regression
The simple linear regression model assumes that our data is generated
according to
STA 371g: Statistics and Modeling
i Normal(0, 2 )
Yi = 0 + 1 Xi + i
Lecture 18: Midterm Review
or, equivalently,
Yi |Xi Normal(0 + 1 Xi , 2 )
Sinea
Obtaining extra information?
Extra information can help us make more accurate predictions, and more
profitable choices.
I
STA 371g: Statistics and Modeling
Spending a summer doing an internship can help you decide whether
you want a career in consulting.
Conditional, Joint and Marginal Distributions
Last lecture we introduced the idea of conditional, joint and marginal
probability distributions.
STA 371g: Statistics and Modeling
I
Lecture 3: Bayes Law; Expectation and Variance.
P(Y = y ) and P(X = x) are
Modeling, Sampling and Estimating
I
Last lecture, we looked at continuous probability distributions in
particular, the normal distribution.
STA 371g: Statistics and Modeling
Lecture 5: Modeling, sampling and estimating
X N(,
Sinead Williamson
The Universi
Building a decision tree
Last time, we were looking at the bidding strategy of a scientific
instruments company
STA 371g: Statistics and Modeling
Lecture 7: Using PrecisionTree
I
Cost to prepare a bid: $5000.
I
Cost to supply instruments: $95,000.
I
Proba
Getting Started
STA 371g: Statistics and Modeling
Lecture 1: Overview and Logistics; Random variables
Sinead Williamson
The University of Texas McCombs School of Business
Your instructor:
Prof. Sinead Williamson
email:
sinead.williamson@mccombs.utexas.edu
Introduction
Materials
Assignments
Tests
Survey
Data and Variables
Welcome to STA 309
Elementary Business Statistics
Betsy Greenberg
Betsy Greenberg
Elementary Business Statistics
McCombs
Introduction
Materials
1
Introduction
Staff
Course Goals
2
Material
What is random?
Probability
Probability Rules
Randomness and Probability
Betsy Greenberg
Betsy Greenberg
Elementary Business Statistics Randomness and Probability
McCombs
What is random?
1
What is random?
2
Probability
3
Probability Rules
Probability
Bets