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58. Piece-rate systems are widely debated incentive payment plans. In a recent study of loan officer effectiveness, the following piece-rate system was examined:

%of goal reached
<80
80
100
120
Incentive
n/a
\(4,000with an additional \)125added per percentage point from 81-99%
\(6,500with an additional \)125added per percentage point from 101-119%
\(9,500with an additional \)125added per percentage point from 121%

If a loan officer makes 95%of his or her goal, write the linear function that applies based on the incentive plan table. In context, explain the

y-intercept and slope.

Short Answer

Expert verified

The acquired linear equation is y=4000+125xand when replace xwith 95%, received the desired accumulated sum for the loan officer, which assembles95%.

Step by step solution

01

Given information

Piece-rate systems are widely debated incentive payment plans. A loan officer makes 95%of his or her goal, with the linear function that applies based on the incentive plan table.

02

Explanation

Linear regression is a linear equation of two variables from which one is liberated, and another is dependent on the other. Let Xis independent variable and Y is dependent. Hence, linear equation is,
Y=a+bX,
where aand bare coefficients, ais intercept and b is a slope.
To complete the linear equation of loan officer point, which creates
95%of his or her goals. From the previous table,4types of goal reached: less than 80,81-99%,100-119%and larger than 121%. Since, to complete the linear equation for effectiveness 95%of goals then use information in table under 80.

03

Explanation

The loan officer will get4000dollars and 125 dollars per percentage point. Now the equation of all acquired sum is provided by:
y=a+bx

=4000+125x

where intercept a=4000is the spot sum which he receives for his job, and the slope is a value that represents the rate of change betweenyand xand in this case this is 125dollars per percentage point. Variable X represents the percentage point which he/she makes.
To get the accumulated sum for the loan officer, which causes
95%of his or her goals, require to substitute Xwith 95%in the earlier equation.

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