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58

Expert-verified
Found in: Page 720

### Introductory Statistics

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$$80$100120Incentiven/a$4,000$ with an additional $125$added per percentage point from $81-99%$$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 $y=4000+125×x$ and when replace $\mathrm{x}$ with $95%$, received the desired accumulated sum for the loan officer, which assembles$95%$.

See the step by step solution

## Step 1: 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.

## Step 2: 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 $80$ .

## Step 3: Explanation

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

$=4000+125×x$

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.