Coefficient of determination, Mathematics

It refers to the ratio of the explained variation to the total variation and is utilized to measure the strength of the linear relationship. The stronger the linear relationship the closer the ratio will be to one.

Coefficient determination = Explained variation/Total variation

Illustration of Rank Correlation Coefficient

In a beauty competition two assessors were asked to rank the 10 contestants by using the professional assessment skills. The results obtained were described as shown in the table below as:

Contestants

1st assessor

2nd assessor

A

6

5

B

1

3

C

3

4

D

7

6

E

8

7

F

2

1

G

4

8

H

5

2

J

10

9

K

9

10

REQUIRED

Compute the rank correlation coefficient and thus comment briefly on the value acquired

 

 

 

d

d2

A

6

5

1

1

B

1

3

-2

4

C

3

4

-1

1

D

7

6

1

1

E

8

7

1

1

F

2

1

1

1

G

4

8

-4

16

H

5

2

3

9

J

10

9

+1

1

K

9

10

-1

1

 

 

 

 

Σ d2 = 36

 

The rank correlation coefficient R

            R = 1 -  {(6Σd2)/(n(n2 -1))}

                        = 1 -  {(6(36))/(10(102 -1))}

                        = 1 -  (216/990)

                        = 1 - 0.22

                        = 0.78

Comment: because the correlation is 0.78 it implies that there is high positive correlation among the ranks awarded to the contestants. 0.78 > 0 and 0.78 > 0.5

Illustration

Contestant

1st assessor

2nd assessor

d

d2

A

1

2

-1

1

B

5 (5.5)

3

2.5

6.25

C

3

4

-1

1

D

2

1

1

1

E

4

5

-1

1

F

5 (5.5)

6.5

-1

1

G

7

6.5

-0.5

0.25

H

8

8

0

0

 

 

 

 

Σ  d2 = 11.25

Required: Complete the rank correlation coefficient

∴ R = 1 - {(6Σd2)/(n(n2 -1))}

 

= 1 -  {(6(11.25))/(8(63))}

= 1 -  (67.5/507)

= 1 - 0.13

= 0.87

This shows high positive correlation

Posted Date: 2/18/2013 5:27:44 AM | Location : United States







Related Discussions:- Coefficient of determination, Assignment Help, Ask Question on Coefficient of determination, Get Answer, Expert's Help, Coefficient of determination Discussions

Write discussion on Coefficient of determination
Your posts are moderated
Related Questions

The angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aX

I need assignment help for Equal Matrices. can you please define Equal Matrices?

Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we

Children Learn From Each Other :  The other day I had gone to a, nearby school to observe the teacher-children interaction. The children were working on a problem that the teacher

Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f

is this free for LIFE that means forever never ever going to pay

what is an pie chart

How is the probability distribution of a random variable constructed? Usually, the past behavior of the variable is studied and the frequency distribution of the past data is form

Use Newton's Method to find out an approximation to the solution to cos x = x which lies in the interval [0,2].  Determine the approximation to six decimal places. Solution