Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Problem Set 1
Q2
(a)
Minimum case is when A B. In that case, P r(A B) = 0.9. While the maximum case
is when A B = U , the whole set. Then P r(A B) = 1.
(b)
P (A B) = P (A) + P (B) P (A B) = P (A B c ) + P (B)
= P (A)P (B c ) + P (B) = P (A)[1 P (B)] + P (
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Question 2
a) m1<lm(formula = ed ~ dist, data = college)
> coef(lm(formula = ed ~ dist, data = college)
(Intercept)
dist
13.95585611 0.07337271
The reported coefficients suggest that the greater the distance from high school to
college, the fewer the ye
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Introduction to Econometrics
The statistical analysis of economic (and related) data
SW Ch 123
1/ 60
Brief Overview of the Course
Economic theory suggests important relationships, often with
policy implications, but virtually never suggests quantitative
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Data Transformation
with dplyr Cheat Sheet
dplyr functions work with pipes and expect tidy data. In tidy data:
A B C
&
Each variable is
in its own column
A B C
pipes
Each observation, or
case, is in its own row
x %>% f(y)
becomes f(x, y)
Summarise Cases
T
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
CHAPTER 3
DESCRIPTIVE STATISTICS
Based on the slides by D. Zerom, Ph.D.
Learning Goals
Shape (Skewness, symmetry, modality)
Location (mean, median, mode)
Variability/Spread (variance, standard deviation, range, IQR)
Relative Location (zscore)
Empirical R
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
CHAPTER 6
NORMAL PROBABILITY MODEL/
DISTRIBUTION
Learning Goals
Normal Probability Distribution
Population Mean () and Population Standard Deviation ()
zscores
Standard Normal Probability Distribution
Calculating Probabilities
Inverse Problems
Refresher:
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
INTERVAL ESTIMATION
CHAPTER 8: SECTION 2
Learning Goals
Interval Estimation of when is unknown
(Section 8.2)
Inference based on small sample
t distribution
Degrees of freedom
Example #1:
Average credit card balance
executive in a large bank is looking fo
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
CHAPTER 1
DATA AND STATISTICS
Learning Goals
Data
Statistics
Descriptive vs. Inferential Statistics
Types of Descriptive Statistics
Elements of Inferential Statistics
Data Collection Methods
Inference errors from nonrandom samples
SURVEY
A random sample o
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
AN INTRODUCTION TO RANDOM
VARIABLES
TO BE READ BEFORE CHAPTER 6
Based on the slides by Dr. Zerom
Learning Goals
Inferential statistics
Probability
Random Variable
Probability Distribution
Continuous and Discrete Random Variables
In Chapter 1
In Chapter 1,
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
INTERVAL ESTIMATION
CHAPTER 8: SECTIONS 3 AND PART OF 4
Learning Goals
Sample Size (n) determination in Interval Estimation of when is
known
(Section 8.3)
Sample Size (n) determination in Interval Estimation of p
(Section 8.4)
Revisit:
ME versus sampl
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
INTERVAL ESTIMATION
CHAPTER 8: SECTIONS 1 AND 4
Based on the slides by Dr. Zerom
Learning Goals
Interval Estimation of when is known
(Section 8.1)
Interval Estimation of p
(Section 8.4)
Interval Estimation of
when is known
Example #1:
Average Travel Time
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
WHY SAMPLING DISTRIBUTIONS?
TO BE READ BEFORE CHAPTER 7
Based on the slides by Dr. Zerom
Learning Goals
Inferential Statistics
Population Versus Sample
Population Parameters ( and p)
Sample Statistic or Point Estimators ( and )
Sampling Distribution
Popul
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
ECON3412 PS5 Solutions
Spring 2017
Question 1
a) We want to estimate the production parameters: , 1 , 2, 3. To estimate using OLS, we must create a linear model. We do so
by taking the natural logarithm of the equation.
ln(Q) = ln(K 1 L2 M 3 eu )
= ln() +
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
ECON3412 PS2 Solutions
Spring 2017
Q1: (Empirical Exercise E3.2)
(a)
We are told that good A and good B have approximately equal market value. Furthermore, since
traders were randomly given one of two sports collectables, subjects should not consistently
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Problem Set 3 Solutions
2 February 2017
Q1
(a)
Ui is all other factors that affect an individual students exam score, and so differs across students.
(b)
Because exam time Xi is randomly assigned the two groups will be mean independent of other factors af
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Problem Set 9: Experiments and QuasiExperiments
Introduction to Econometrics (Spring 2017)
Due: Tuesday, April 25 at the beginning of the lecture
Question 1 (modified from SW 13.7)
Suppose that you have panel data with two periods (t = 1, 2). Let the tre
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Question 1
A popular type of time series model is the socalled Moving Average model, or MA(1). To
describe the model, suppose that u0 , u1 , u2 , . . . are independent and identically distributed
random variables such that ut N (0, 2 ) for all t, and tha
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Midterm Exam Instructions
Introduction to Econometrics, Spring 2017
Prof. Adam Kapor
1. This exam consists of four pages, including this one. Please verify that your copy is
complete.
2. Write your answers into the blue book. You should not need more than
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Final Exam
Introduction to Econometrics, Spring 2015
Prof. Christoph Rothe
1. This exam consists of 10 pages, including this one. Please verify that your copy is
complete.
2. Write your answers into the blue book. You should not need more than one. No cre
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Final Exam Instruction
Introduction to Econometrics Spring 2013
1. Write your answers in the blue book. You should not need more than one. No credit is given
for answers not in the blue book.
2. You are allowed a calculator and one page (on both sides) of
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
PS9 Solutions
Introduction to Econometrics (Spring 2017)
April 29, 2017
Question 1:
Yit = i + 1 Xit + 0 Dt + vit
a) Dt allows for changes over time that are not due to the treatment, eg: in a medical example people
may recover on their own without the dru
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Problem Set 8: Instrumental Variables
Introduction to Econometrics (Spring 2017)
Due: Tuesday, April 18 at the beginning of the lecture
Question 1
Consider the simple regression model
Y = 0 + 1 X + U
and let Z be a binary instrumental variable for X. Show
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Problem Set 6
Q1
(a)
Repeated crosssection is just a cross section data with several time periods but Panel
data tracks the same guys for several periods in each crosssection data.
(b)
All three cases lead to nonzero correlation between regressors and
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Choosing the Right Communication Channel
Introduction
As a public health crisis evolves beyond 24 to 48 hours, the demand for information outside
traditional media channels (radio, TV, newspaper, and news Web sites) increases, and public
information offic
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
CHAPTER TWENTY
AGENCY
An agency exists when one party, the agent, agrees to represent or act for
another party, the principal.
The principal has the right to control the agents conduct in matters
entrusted to the agent
Only through agents can a corporatio
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Where Coffee and Friends Make the Perfect Blend
8873 Orange Dr. Santa Ana, CA 77128
Phone:(714)5629823 Email: [email protected]
Table of Contents
Executive Summary .
Mission Statement
Description of Business .
Management Team
Problem
Solution
Location
Probability and Statistical Methods in Business and Economics
ISDS 361A

Fall 2011
Questions for Audience Analysis
The following questions provide a framework
for audience analysis:
1. What will the audiences initial reaction be to the
message?
2. How much information does the audience need?
3. What obstacles must you overcome?
4. What