Short Answer

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 $x$ with $95 %$ , received the desired accumulated sum for the loan officer, which assembles $95 %$ .

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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,
$Y = a + b X,$ 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: $y = a + b \times x$

$= 4000 + 125 \times x$

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 $y$ and $x$ and in this case this is $125$ dollars 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 $X$ with $95 %$ in the earlier equation.

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$%$ 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 $121 %$

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