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58

Expert-verifiedFound in: Page 720

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

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

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$95\%$.

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.

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 $80$ .

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.

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