Coefficient of determination, Mathematics

Assignment Help:

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


Related Discussions:- Coefficient of determination

Quadric surfaces, identify 4 sketch the quadric surfaces

identify 4 sketch the quadric surfaces

Business math, David invests $17,000 into an account and at the end of 7 ye...

David invests $17,000 into an account and at the end of 7 years, his account has a balance of $ 26,417.77. What is the interest rate (assuming annual compounding)?

Properties for exponents, The next thing that we must acknowledge is that a...

The next thing that we must acknowledge is that all of the properties for exponents . This includes the more general rational exponent that we haven't looked at yet. Now the pr

Find the derivations of functions, Find the derivatives of each of the foll...

Find the derivatives of each of the following functions, and their points of maximization or minimization if possible. a.  TC = 1500 - 100 Q + 2Q 2 b.  ATC = 1500/Q - 100 +

Determine the property of join in a boolean algebra, Determine that in a Bo...

Determine that in a Boolean algebra, for any a and b, (a Λ b) V (a Λ b' ) = a.  Ans: This can be proved either by using the distributive property of join over meet (or of mee

Machines, descuss the seauencing problem for n jobs on two and three machin...

descuss the seauencing problem for n jobs on two and three machines

Regression, regression line drawn as Y=C+1075x, when x was 2, and y was 239...

regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

#tiword problem proportions, The scale of a map is 0.5 in 25mi the actua...

The scale of a map is 0.5 in 25mi the actual distance between two cities is 725mi write a proportion that represents the relationship how far apart will the cities be on the map

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd