Question

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	$\backslash (4,000$with an additional $\backslash )125$added per percentage point from $81-99\%$	$\backslash (6,500$with an additional $\backslash )125$added per percentage point from $101-119\%$	$\backslash (9,500$with an additional $\backslash )125$added 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

The acquired linear equation is $y=4000+125\times x$and when replace $\mathrm{x}$with $95\%$, received the desired accumulated sum for the loan officer, which assembles$95\%$.

Step-by-step solution

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.

Explanation

Linear regression is a linear equation of two variables from which one is liberated, and another is dependent on the other. Let $X$is independent variable and $Y$ is dependent. Hence, linear equation is,
$Y=a+bX,$
where $a$and $b$are coefficients, $a$is 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,$4$types 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 $80$.

Explanation

The loan officer will get$4000$dollars and $125$ dollars per percentage point. Now the equation of all acquired sum is provided by:
$y=a+b\times x$

$=4000+125\times x$

where intercept $a=4000$is the spot sum which he receives for his job, and the slope is a value that represents the rate of change between$\mathrm{y}$and $\mathrm{x}$and in this case this is $125$dollars per percentage point. Variable $\mathrm{X}$ 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 $X$with $95\%$in the earlier equation.