Using Minitab for Regression Analysis: An extended example
The following example uses data from another text on fertilizer application and crop
yield, and is intended to show how Minitab can be used to generate the statistical
measures discussed in Anders
Chapter 9
Hypothesis Testing
Testing vs. Estimation
Confidence Intervals are used to estimate an unknown population parameter using sample data. A Hypothesis test is used when theory suggests a particular value for an unknown population parameter. The que
A Couple Less-obvious Chapter 7 questions
1) A ski lift is designed with a load limit of 18,000 pounds. It claims to have a capacity of 100
people. Suppose the weights of all the people using the life have a mean of 175 pounds and a
standard deviation of
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Thursday, February 21, 2002.max
Simulation of Estimators
Suppose you want to estimate the center of the normal distribution. Should you use the sample
mean, or the sample median? Lets try it and see. Lets simulate draws from a normal
distribution with mean 10 and standard deviation 2.
M
Answers to Final Exam Review Questions
Question 1: This problem is a Bayes Law problem. The forward tree branches first on will
and wont date George; the second branch is is free and isnt free. When you reverse the
tree you find that the
P( will date Geor
Review Questions to Prepare for the Exam
1)
George Constanza, the character on Seinfeld, is a perpetual loser who keeps
trying. As long-time viewers of the show know, only 10% of the women George
approaches are willing to go out with him. George often wil
Some Formulas neglected in Anderson, Sweeny, and Williams,
with a Digression on Statistics and Finance
Transformations of a Single Random variable:
If you have a case where a new random variable is defined as a linear
transformation of a another random va
x
x=
Formula Sheet: Anderson, Sweeny, and Williams 9th Edition
xi
(3.1)
=
N
i
n
(3.3)
s
bx
=
i
x
g
(3.5)
IQR = Q3 Q1
2
n 1
xy
x y
=
i
g
2
(3.4)
N
(3.6)
standard deviation
100 %
Mean
xi x yi y
s xy =
n 1
s xy
rxy =
sx s y
(3.7)
b
xi x
(3.9)
s
( xi x
Examples of Graphs for Qualitative Data:
In the Anderson, Sweeny, and Williams data sets for Chapter 2, there is a data set showing the
show being viewed by 50 viewers in a Nielsen sample. Click on FILE > OPEN WORKSHEET
and locate the file Nielsen in the
Notes on logarithms
Ron Michener Revised January 2003
In applied work in economics, it is often the case that statistical work is done using the logarithms of variables, rather than the raw variables themselves. This seems mysterious when one first encoun
ADDITIONAL HOMEWORK PROBLEMS: ECON 371
Spring 2008
Chapter 2
Note: Unlike later additional questions, these two questions use data sets provided with
Anderson, Sweeny, and Williams.
1) On page 58 of Anderson, Sweeny, and Williams, read problem 40 and exam
On the next page you'll find an Op-ed essay that appeared in the New York Times, penned by William Safire. Mr. Safire is famously literate. Unfortunately, he is not equally numerate. Can you spot the problem with his handicapping?
New York Times, June 25,
Chapter 3
Descriptive Statistics Numerical Methods
Our goal? Numbers to help us answer simple questions.
What is a typical value? How variable are the data? How extreme is a particular value? Given data on two variables, how closely do they move together?
Chapter 15
Multiple Regression
Learning Objectives
1.
Understand how multiple regression analysis can be used to develop relationships involving one
dependent variable and several independent variables.
2.
Be able to interpret the coefficients in a multip
Screening of asymptomatic women using Mammograms Bayes Law and a cost/benefit analysis There are many misconceptions about the usefulness of mammograms, as well as a considerable amount of misleading information that has been propagated by advocates of ma
Some Calculations to do the Regression example worked by the computer in the handout
Row
xi
yi
( xi x )
1
2
3
4
5
6
7
100
200
300
400
500
600
700
40
50
50
70
65
65
80
yi = 420
( xi x ) ( yi y )
90000
40000
10000
0
10000
40000
90000
x
i
= 2800
(x x )
2
i
Calculating the probability of winning the Virginia Lotto
The Virginia Lotto requires you to pick 6 numbers (without replacement, i.e. no duplicates)
between 1 and 44. To win a prize you must match either 3, 4, 5 or 6 of the randomly selected numbers. Thi
Chapter 3
Descriptive Statistics: Numerical Methods
Learning Objectives
1.
Understand the purpose of measures of location.
2.
Be able to compute the mean, median, mode, quartiles, and various percentiles.
3.
Understand the purpose of measures of variabili
Chapter 4
Introduction to Probability
Learning Objectives
1.
Obtain an appreciation of the role probability information plays in the decision making process.
2.
Understand probability as a numerical measure of the likelihood of occurrence.
3.
Know the thr
Chapter 5
Discrete Probability Distributions
Learning Objectives
1.
Understand the concepts of a random variable and a probability distribution.
2.
Be able to distinguish between discrete and continuous random variables.
3.
Be able to compute and interpre
Chapter 6
Continuous Probability Distributions
Learning Objectives
1.
Understand the difference between how probabilities are computed for discrete and continuous
random variables.
2.
Know how to compute probability values for a continuous uniform probabi
Chapter 7
Sampling and Sampling Distributions
Learning Objectives
1.
Understand the importance of sampling and how results from samples can be used to provide
estimates of population characteristics such as the population mean, the population standard
dev
Chapter 8
Interval Estimation
Learning Objectives
1.
Know how to construct and interpret an interval estimate of a population mean and / or a population
proportion.
2.
Understand and be able to compute the margin of error.
3.
Learn about the t distributio
Chapter 9
Hypothesis Tests
Learning Objectives
1.
Learn how to formulate and test hypotheses about a population mean and/or a population proportion.
2.
Understand the types of errors possible when conducting a hypothesis test.
3.
Be able to determine the
Chapter 10
Statistical Inference about Means and
Proportions with Two Populations
Learning Objectives
1.
Be able to develop interval estimates and conduct hypothesis tests about the difference between two
population means when 1 and 2 are known.
2.
Know t
Chapter 11
Inferences About Population Variances
Learning Objectives
1.
Understand the importance of variance in a decision-making situation.
2
Understand the role of statistical inference in developing conclusions about the variance of a single
populatio
Chapter 14
Simple Linear Regression
Learning Objectives
1.
Understand how regression analysis can be used to develop an equation that estimates
mathematically how two variables are related.
2.
Understand the differences between the regression model, the r
Answers to additional paper and pencil Questions
Please bring any errors to my attention
Fall 2004
Chapter 4
Question 1
b
g bg bg b g
.6 =.5 + Pb B g 0
.1 = Pb B g
P b A B g = P b Ag + P b B g P b A B g
.6 =.5 + Pb B g.5 Pb B g
.2 = Pb Bg
P b A B g = P b