Exhibit 4-1 . A large data set on Toledo workers was collected and the first thr

Question

Exhibit 4-1. A large data set on Toledo workers was collected and the first three workers are characterized by

Worker

Age

Hourly Wage

Female

Union

High School

1

33

$20

0

0

1

2

30

$24

0

1

1

3

36

$16

1

0

0

where Female=1 if a worker is a female Female=0 otherwise

   Union=1 if a worker belongs to a union    Union=0 otherwise

   High school=1 if a worker has a high school degree High school=0 otherwise

For the entire data set the average age is 32, the standard deviation of the age is 8, the average hourly wage is $18, and the standard deviation of the hourly wage is $5

Refer to Exhibit 4-1. What is the matching coefficient for Workers 1 and 3 based on Female, Union, and High School?

1

1/3

2/3

0

Question 15

Refer to Exhibit 4-1. What is Jaccard’s coefficient for Workers 2 and 3 based on Female, Union, and High School?

1/3

2/3

1/2

0

Thank you for all of your help.

Worker

Age

Hourly Wage

Female

Union

High School

1

33

$20

0

0

1

2

30

$24

0

1

1

3

36

$16

1

0

0

Explanation / Answer

Question 14 Refer to Exhibit 4-1. What is the matching coefficient for Workers 1 and 3 based on Female, Union, and High School?

we can see that worker 1 is male(0), doesn't belong to union(0) and has a high school degree(1). For worker 2 , we can say that she is a female (1), doesn't belong to union (0) and doesn't has a high school degree(0) .

So, Matching coefficient = Number of matching attributes/ No. of total attributes

= (M00 + M11)/(M00 + M10 + M01 + M11)

where:

M11 is the total number of attributes where A and B both have a value of 1.

M01 is the total number of attributes where the attribute of A is 0 and the attribute of B is 1.

M10 is the total number of attributes where the attribute of A is 1 and the attribute of B is 0.

M00 is the total number of attributes where A and B both have a value of 0.

Here M00 = 1 , M10 = 1 , M01 =1 M11 = 0 [ Here A and B are worker 1 and worker 3]

So Matching Coeffienct = 1/ ( 1+ 1 + 1) = 1/3 [ Option B]

Question 15 Refer to Exhibit 4-1. What is Jaccard’s coefficient for Workers 2 and 3 based on Female, Union, and High School?

we can see that worker 2 is male(0), belong to union(1) and has a high school degree(1). For worker 2 , we can say that she is a female (1), doesn't belong to union (0) and doesn't has a high school degree(0) .

So, Jacckard Coefficnet = Number of matching attributes/ No. of total attributes

= (M11)/(M10 + M01 + M11)

where:

M11 is the total number of attributes where A and B both have a value of 1.

M01 is the total number of attributes where the attribute of A is 0 and the attribute of B is 1.

M10 is the total number of attributes where the attribute of A is 1 and the attribute of B is 0.

Here M10 = 2 , M01 =1 M11 = 0 [ Here A and B are worker 1 and worker 3]

So Matching Coeffienct = 0/ ( 2+ 1 + 0) = 0 [ option D ]

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