Problem Set 1
1. After the graduation ceremonies at a university, six graduates were asked
whether they were in favor of (identified by 1) or against (identified by 0)
abortion. Some information about these graduates is shown below.
Graduate
Gender
Age
Ab
10.1. Population Mean: Large Sample Case ( n 30 )
Motivating example:
In the survey conducted by CJW, Inc., a mail-order firm, the satisfaction scores
(1~100) of 100 customers (n=100) are obtained. Suppose = 20 is known. Also,
x = 82 , x =
n
=
20
100
= 2.
Chapter 3 Descriptive Statistics: Numerical
Methods
Suppose
y1, y2 ,K, yN
are all the elements in the population and
are the sample drawn from
y1, y2 ,K, yN ,
x1 , x2 ,K, xn
where N is referred to as the
population size and n is the sample size. In this c
14.6 Multiple Regression
Motivating Example:
Heller Company manufactures lawn mowers and related lawn equipment. The
managers believe the quantity of lawn mowers sold depends on the price of the
mower and the price of a competitors mower. We have the foll
Chapter 3 Descriptive Statistics: Numerical
Methods
Suppose
y1 , y 2 , , y N
the sample drawn from
are all the elements in the population and
x1 , x 2 , , x n
are
y1 , y 2 , , y N , where N is referred to as the population
size and n is the sample size. I
14.6 Multiple Regression
Motivating Example:
Heller Company manufactures lawn mowers and related lawn equipment. The
managers believe the quantity of lawn mowers sold depends on the price of the
mower and the price of a competitors mower. We have the foll
3.5 The Weighted Mean and Grouped Data:
Weighted Mean:
n
xw =
i =1
n
i =1
wixi
wi
.
Note: when data values vary in importance, the analyst must choose
the weight that best reflects the importance of each data value in the
determination of the mean.
Exampl
14.5 Residuals
The residuals are defined as
ei = y i y i = y i b0 b1 xi , i = 1, 2 , K , n.
If the least square estimate is a sensible estimate, ei can be regarded as
the estimate of i ,
ei = yi yi = 0 + 1xi + i b0 b1xi
= (0 b0 ) + (1 b1 )xi + i
i
Thus,
3.5 The Weighted Mean and Grouped Data:
Weighted Mean:
n
w
x
1
xw = i =n
i
i
w
i=
1
.
i
Note: when data values vary in importance, the analyst must choose
the weight that best reflects the importance of each data value in the
determination of the mean.
Ex
14.5 Residuals
The residuals are defined as
ei = yi yi = yi b0 b1 xi , i = 1,2, , n.
If the least square estimate is a sensible estimate, ei can be regarded as
the estimate of i ,
ei = yi yi = 0 + 1 xi + i b0 b1 xi
= ( 0 b0 ) + ( 1 b1 ) xi + i
i
Thus, th
Chapter 14 Regression Analysis
Motivating Example:
The following data were collected from a sample of 10 Pizza restaurants located near
college campuses.
Student Population (1000s)
xi
Quarterly Sales ($1000s)
2
6
8
8
12
16
20
20
22
26
yi
58
105
88
118
117
5.1. Experiments, Counting Rules, and Probabilities
Experiment: any process that generates well-defined outcomes.
Example:
Experiment
Outcomes
Toss a coin
Roll a dice
Play a football game
Rain tomorrow
Head, Tail
1, 2, 3, 4, 5, 6
Win, Lose, Tie
Rain, No r
4.1 Crosstabulations and Scatter Diagrams:
The crosstabulation (table) and the scatter diagram (graph) can help us understand the
relationship between two variables.
1. Crosstabulations
Example:
Objective: explore the association of the quality and the pr
Problem Set 2
1. You are given the following 10 observations on two variables X and Y.
X
1
5
6
4
2
8
9
1
6
8
8
15
20
12
10
20
26
5
18
26
Y
(a) Develop a scatter diagram for the relationship between X and Y.
(b) According to the scatter diagram, what relat
5.1. Experiments, Counting Rules, and Probabilities
Experiment: any process that generates well-defined outcomes.
Example:
Experiment
Toss a coin
Roll a dice
Play a football game
Rain tomorrow
Outcomes
Head, Tail
1, 2, 3, 4, 5, 6
Win, Lose, Tie
Rain, No r
Problem Set 2
1. You are given the following 10 observations on two variables X and Y.
X
Y
1
8
5
15
6
20
4
12
2
10
8
20
9
26
1
5
6
18
8
26
(a) Develop a scatter diagram for the relationship between X and Y.
(b) According to the scatter diagram, what relat
4.2 Numerical Measures of Association:
There are several numerical measures of association. We first introduce the covariance
of two variables.
(I)
Covariance:
Suppose we have two populations,
population 1:
y1, y2,K yN
,
and population 2:
w1 , w2 ,K, wN .
4.2 Numerical Measures of Association:
There are several numerical measures of association. We first introduce the covariance
of two variables.
(I)
Covariance:
Suppose we have two populations,
population 1:
y1 , y 2 , , y N
and population 2:
w1 , w2 , , w
Problem Set 1
1. After the graduation ceremonies at a university, six graduates were asked
whether they were in favor of (identified by 1) or against (identified by 0)
abortion. Some information about these graduates is shown below.
Graduate
Gender
Age
Ab
4.1 Crosstabulations and Scatter Diagrams:
The crosstabulation (table) and the scatter diagram (graph) can help us understand the
relationship between two variables.
1. Crosstabulations
Example:
Objective: explore the association of the quality and the pr
Chapter 14 Regression Analysis
Motivating Example:
The following data were collected from a sample of 10 Pizza restaurants located near
college campuses.
x
Student Population (1000s)
Quarterly Sales ($1000s)
i
2
6
8
8
12
16
20
20
22
26
yi
58
105
88
118
11
3.4 Measures of Relative Location:
z-score is the quantity which can be used to measure the relative location of the data.
Z-score, referred to as the standardized value for observation i, is defined as
zi =
Note:
z i is the number of standard deviation x
14.4 Prediction
The fitted regression equation: y = b0 + b1 x = y + b1 ( x x ) . ,
Based on the fitted equation, we have the following point estimate and
confidence interval estimate of the mean value of y for a given value of x.
Point estimate of E ( y p
14.1 Least Squares Method
The data in the motivating example can be modeled by
yi = 0 + 1 xi + i , i = 1,K,10 .
0
is the basic quarterly sales,
1
reflects the increased or decreased
quarterly sales per student population unit (1000) and
unexpected variati
3.1 Measure of Location:
Example 1:
Suppose the following data are the scores of 10 students in a quiz,
1, 3, 5, 7, 9, 2, 4, 6, 8, 10.
Some measures need to be used to provide information about the performance of the
10 students in this quiz.
(I) Mean:
n
14.1 Least Squares Method
The data in the motivating example can be modeled by
y i = 0 + 1 xi + i , i = 1, ,10 .
0
is the basic quarterly sales,
1
reflects the increased or decreased
quarterly sales per student population unit (1000) and
unexpected variat
Chapter 2 Descriptive Statistics: Table and Graph
The logical flow of this chapter:
Summarizing qualitative data using tables and graphs (2.1)
Summarizing quantitative data using tables and graphs (2.2)
Exploratory data analysis using simple arithmetic an
Chapter 13 Comparisons Involving Proportions
The logical flow of this chapter:
Estimation & testing hypothesis about the difference between
the proportions of two populations (11.1)
Hypothesis tests for proportions of a multinomial population
(11.2)
Testi
Chapter 2 Descriptive Statistics: Table and Graph
The logical flow of this chapter:
Summarizing qualitative data using tables and graphs (2.1)
Summarizing quantitative data using tables and graphs (2.2)
Exploratory data analysis using simple arithmetic an
Chapter 13 Comparisons Involving Proportions
The logical flow of this chapter:
Estimation & testing hypothesis about the difference between
the proportions of two populations (11.1)
Hypothesis tests for proportions of a multinomial population
(11.2)
Test