Skip to document
Welcome to StudocuSign in to access the best study resources
Guest user
0followers
HomeMy LibraryAsk AI
  • You don't have any recent items yet.
My Library
  • You don't have any courses yet.
  • You don't have any books yet.
  • You don't have any Studylists yet.

STA450 MAR2022 - Topic TWO

ukgb
Course

Data Communication Networking (ITT300)

184 Documents
Students shared 184 documents in this course
Academic year: 2020/2021
Uploaded by:
Anonymous Student
This document has been uploaded by a student, just like you, who decided to remain anonymous.
Universiti Teknologi MARA

Recommended for you

Comments

Please sign in or register to post comments.

Students also viewed

Related documents

Preview text

TOPIC TWO: CORRELATION ANALYSIS

2 Scatter plot and its uses.

A scatter plot is a plot of the values of Y versus the corresponding values of X:

 Vertical axis: variable Y – usually the response variable

 Horizontal axis: variable X – usually some variable we suspect may be related to the

response.

The first step in regression analysis is to construct a scatter diagram. This is a graphical plot of

the dependent and independent variables.

2.1 Uses of a scatter diagram

a) To determine if there is a linear relationship between the dependent and independent

variable.

b) To determine the type of the relationship among variables. Is it a positive or negative

relationship?

c) To identify the strength of relationship between dependent variable and independent

variable. Is it strong or weak relationship?

d) To determine the existence of outlier

2.1 Types of scatter diagrams

Example 1: An editor for a publishing company believes a major part of the cost of textbooks is

the cost of paper. The editor wants to investigate the relationship between the cost of a

textbook and its number of pages. He randomly selects 12 books from a university’s bookstore,

and records the selling price and the number of pages for each textbook. The data appears

below.

Price (in RM) No of Pages

155 844

150 727

135 360

160 915

130 295

150 706

140 410

153 905

165 1058

154 865

142 677

158 912

Obtain a scatter diagram for the above data.

Other examples:

r = +.3 r = +

Examples of Approximate

r Values

y

x

y

x

y

x

y

x

y

x

r = -1 r = - r = 0

2 Purpose of Correlation Analysis.

To make a prediction about one variable based on what we know about another variables.

2 Correlation Coefficient

The formula for the correlation coefficient is as follows:

   

XY

XX YY 2 2

2 2

X Y

SS XY

r n

SS SS X Y

X Y

n n

 

 

 

     

       

    

where

XY

X Y

SS XY

n

 

  

 

2

2

XX

X

SS X

n

  

 

2

2

YY

Y

SS Y

n

  

The following drawing summarizes the strength and direction of the correlation coefficient.

2 Testing the significance of the linear relationship between the independent and

dependent variables.

Sometimes the value of r may be reasonably high but we may still want to determine if the

relationship is significant. We then use the following hypothesis.

2.5 Two Tailed Test

A two-tailed test is used when we want test whether there is a significant relationship between

the dependent and independent variable.

Hypothesis:

0
1
H : 0 (There is no significant linear relationship between X and Y)
H : 0 (There is a significant linear relationship between X and Y)
 
 

Test Statistic:

2
r n 2
t
1 r

Critical Value at significance level α

c ,n 2
2
t t

 @ c

2 ,n 2
t t
 

Decision Rule:

If t  t c , H 0 is rejected where t  tc  t   tc or t tc

If t  t c , H 0 is NOT rejected where t  tc   tc  t tc

Conclusion:

If reject H 0 , there is a significant linear relationship between X and Y

Now test whether there is a significant linear relationship between the number of calls made by

the sales representatives and the number of machines sold.

2.5 One Tailed Test

We can also test whether there is a significant positive or negative relationship between the

two variables.

To test whether r is positive

Hypothesis

: 0

: 0

####### 1

####### 0

 

H

H

Test Statistic

2
r n 2
t
1 r

Critical value at sig. level α

c ,n 2
2
t t 

Decision

If t t c , H 0 is rejected

If t t c , H 0 is NOT rejected

To test whether r is negative

Hypothesis

: 0

: 0

####### 1

####### 0

 

H

H

Test Statistic

2
r n 2
t
1 r

Critical value at sig. level α

c ,n 2
2
t t 
 

Decision

If t  tc H 0 is rejected

If t  t c , H 0 is NOT rejected

Example 4: Based on Example 1, test for a significant linear relationship between the price and

number of pages among textbooks. Use α=0.

2 Coefficient of determination.

The coefficient of determination, r 2 is the proportion of variation in the dependent variable (Y)

that is explained by the variation in the independent variable (X).

 

2 2

r  correlation coefficient or 2

SSR SSE
r 1
SST SST
  

Interpretation:

The percentage of the total variation in Y is explained by X. The balance is explained by the

others factors.

Example 5: Based on Example 1, calculate the coeeficient of determination and interpret the

value obtained.

Was this document helpful?

STA450 MAR2022 - Topic TWO

Course: Data Communication Networking (ITT300)

184 Documents
Students shared 184 documents in this course

University: Universiti Teknologi MARA

Was this document helpful?
STA450: FUNDAMENTALS OF REGRESSION ANALYSIS
1
TOPIC TWO: CORRELATION ANALYSIS
2.1 Scatter plot and its uses.
A scatter plot is a plot of the values of Y versus the corresponding values of X:
Vertical axis: variable Y – usually the response variable
Horizontal axis: variable X – usually some variable we suspect may be related to the
response.
The first step in regression analysis is to construct a scatter diagram. This is a graphical plot of
the dependent and independent variables.
2.1.1 Uses of a scatter diagram
a) To determine if there is a linear relationship between the dependent and independent
variable.
b) To determine the type of the relationship among variables. Is it a positive or negative
relationship?
c) To identify the strength of relationship between dependent variable and independent
variable. Is it strong or weak relationship?
d) To determine the existence of outlier
2.1.2 Types of scatter diagrams

Students also viewed

Related documents