Assignment 2
INCOME AND MAGAZINE SUBSCRIPTION DATA
A sample of 50 households in an upper middle class community was taken and the
following measurements were obtained:
Variable 1 =
X i annual income in household i in thousands of dollars.
Variable 2 =
Yi
Assignment 22
FORECASTING PROFITS IN SUPERMARKETS
A company wishes to predict profit Y (in thousands of dollars) for supermarkets with
independent variables of total sales (in thousands of dollars) of (i) X1 = foods and
(ii) X2 = nonfoods. The data are:
S
Assignment 4
b. P(B) t0.HI=.59
c. P(AoB) .37 .H = .ISI7
d. P(AuB) .37+-Hl=.78-,\S\7:,Q,293
e. P(AUB) .63 +,5q -(.65-,5q)=.8183
f. P(AnB) .93 - . 501 3.37l7
2. 'The probabilities that O, l, 2, 3, 4, or at least 5 applicants for a carpenters job will apply
Assignment 12
OPTIMUM ALLOCATION OF INVESTMENTS
The joint distribution of the rates of return (in %) of an income fund (X) and a
money market fund (Y) is given as follows:
XY
5
7
9
11
5
.04
.06
.10
.20
6
.06
.08
.10
.06
7
0
.06
.10
.04
8
0
0
0
.10
Show th
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2. Assignment4,page634inthenotes,doproblems46.Hint:make2by2tables,
labelingtherowsA,AandthecolumnsB,B(IamusingAtoindicateAcomplement.
1.
If
A and B
a.
b.
c.
d.
2.
Given
a.
b.
c.
d.
e.
3.
areindependentevents
Assignment 14
OPTIUM ALLOCATIONS OF INVESTMENTS B
The joint distribution of the rates of return on an equity fund (X) a money market
fund (Y) and an income fund (Z) has a multivariate normal distribution with the following
means, standard deviations and c
1.
2.
3.
Im really stumped on this one. Could it be explained? Thank you!
37
Assignment 1
APPLICATIONS OF LOCATION MEASURES FOR DISTRIBUTIONS
Ten thousand families are randomly selected in a survey of the United States to determine
their annual income. Th
Assignment 13
OPTIMUM ALLOCATION OF INVESTMENTS A
The joint distribution of the rates of return (in %) of an equity fund (X) and a
money market fund (Y) is given as follows:
XY
0
5
10
15
1. Show that
5
0
0
.2
.2
6
0
0
.1
.2
7
.1
.1
0
0
8
0
.1
0
0
X 10, Y
CLASS I
Introduction to
Descriptive Statistics
Class 1: What well be discussing
p Course
basics
p Descriptive vs. inferential statistics
p Levels of measurement
p Application: descriptive statistics
using numbers, tables, graphics
p Practice Problems
Cour
SAMPLING LAB
Name: _
Instructions: This lab helps to demonstrate the ideas of sampling. Select 5 cards
at random (without replacement) from the deck of index cards.
Record your sample values:
Characteristics of your sample (fill in later):
The sample mean
21. MULTIPLE REGRESSION
(1) Describing the relationship.
Multiple regression provides a method of predicting a
response variable y from two or more explanatory x
variables.
Salary (y) of company employees may depend on several
factors, such as years of e
Statistics plays a key role in Business. A few examples:
1. INTRODUCTION
"Statistics is data analysis, together with everything you need
to do data analysis. -John Tukey
Accounting: Measurememt of Earnings Surprise
"What is real, and what is an illusion?
20. SIMPLE LINEAR REGRESSION V
Consider the Salary vs. Height example.
Using The Regression Model For
Estimation and Prediction
Fitted Line Plot for Salary vs. Height
Salary = - 902.2 + 100.4 Height
6500
Once we are convinced that the model is reasonable,
3. PROBABILITY
"Anything that is measured contains some degree of
randomness. -Cliff Hurvich
Probability
Allows you to handle randomness (uncertainty)
Is a central concept for risk management
Is used for calculating expectations
Do you agree?
Is key f
11. CONFIDENCE INTERVALS FOR
THE MEAN; KNOWN VARIANCE
We assume here that the population variance 2 is known.
This is an unrealistic assumption, but it allows us to give a
simplified presentation which reveals many of the important
issues, and prepares us
18. SIMPLE LINEAR REGRESSION III
US Domestic Beers: Calories vs. % Alcohol
225
Fitted Values and Residuals
The y i are called fitted values.
They are the values of y which would be predicted by the
estimated linear regression model, at the observed values
6. THE BINOMIAL DISTRIBUTION
Eg: For 1000 borrowers in the lowest risk category (FICO
score between 800 and 850), what is the probability that at
least 250 of them will default on their loan (thereby rendering
the bank insolvent)?
Eg: Dave interviews with
9. SAMPLING AND
STATISTICAL INFERENCE
We often need to know something about a large population.
Eg: What is the average number of hours per week devoted to
online social networking for all US residents?
Its often infeasible to examine the entire populatio
15. p-VALUES
A common complaint about Hypothesis Testing: The choice of
the significance level is essentially arbitrary.
To make matters worse, the conclusions (Reject or Dont Reject
H0) depend on what value of is used.
Eg: In the Quarter Pounders example
22. INFERENCE FOR
MULTIPLE REGRESSION
We can interpret most of the Minitab Multiple Regression output as
we did in the simple regression case.
Testing For Significance of an Individual Parameter
The Minitab t-statistics (T) can be used for testing that a
17. SIMPLE LINEAR REGRESSION II
The Model
In linear regression analysis, we assume that the relationship
between X and Y is linear. This does not mean, however, that Y
can be perfectly predicted from X. In real applications there will
almost always be som
2. Z-SCORES AND
THE EMPIRICAL RULE
Eg 1: The earnings per share (EPS) for FedEx in the May quarter
were $2.66, failing to meet analysts' expectations of $2.70
(consensus forecast). The earnings surprise for FedEx was
2.66 2.70 = .04. Is this bad compared
14. MORE HYPOTHESIS TESTING
The Logic Behind Hypothesis Testing
For simplicity, consider testing H0: = 0 against the two-sided
alternative HA: 0.
Even if H0 is true (so that the expectation of X is 0), x will
probably not equal 0 exactly.
Instead, we need
16. SIMPLE LINEAR REGRESSION I
Often, we wish to study the relationship between two variables:
GMAT Scores and Grade Point Averages of First-Year
Business School Students.
Current CPI, Unemployment in 2 Years.
Movie Budget, Total Gross.
Height, Salary
5. EXPECTED VALUE AND VARIANCE
FOR DISCRETE RANDOM VARIABLES
For a best 4 out of 7 series between two equally-matched teams,
what should the average length of the series be?
Duration of series
4
5
6
7
Probability
0.125
0.25
0.3125
0.3125
If we repeatedly
4. DISCRETE PROBABILITY
DISTRIBUTIONS
A random variable is the result of a random experiment in the
abstract sense, before the experiment is performed.
Random Variable: A quantity that takes on different values
depending on chance.
The value the random
19. SIMPLE LINEAR REGRESSION IV
The Coefficient of Determination, R2
Recall the Salary vs. Height data.
Fitted Line Plot for Salary vs. Height
Salary = - 902.2 + 100.4 Height
Once we have decided that is not zero, so that a linear
relationship seems to ex
7. CONTINUOUS DISTRIBUTIONS
Some distributions are discrete; others are continuous. Whats the
difference?
A random variable has a continuous distribution if it can take any
real value in some interval.
Examples of intervals: The set of all real numbers
Th
B01.1305.03
MIDTERM
Name:_
This is the answer sheet. Circle the choice which best answers each question on
the exam. Do not write anything else on this sheet (besides your name and the
circles). When you are finished, hand in just this answer sheet. You c
SOLUTIONS TO MIDTERM
VERSION 1
1) Let A=cfw_Employee smokes, B=cfw_Employee listens to music. We have
P(A)=.2, P(B)=.75 and P(A|B)=.15. We need P(AB)=P(B)P(A|B)=(.75)
(.15)=.1125. Answer is D.
2) We have P(B|A)=P(AB) /P(A)=P(cfw_2,4)/P(cfw_1,2,4)=(2/6)/(3