A company has observed that there is a linear relationship between indirect labo

Question

A company has observed that there is a linear relationship between indirect labor expense (ILE) , in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 18 months aregiven in the file below.

Treating ILE as the response variable, use regression to fit a straight line to all 18 data points.

Based on your results, If direct labor hours (DLH) increases by one hour, the indirect labor expense (ILE), on average, increases by approximately how much?

Place your answer, rounded to 2 decimal places, in the blank. Do not use any stray punctuation marks or a dollar sign. For example, 34.56 would be a legitimate entry.

File Contents Below:

DLH:20,25,22,23,20,19,24,28,26,29,27,25,28,32,35,34,30,36

ILE: 361,400,376,384,361,360,427.2,458.4,450.8,475.2,462.6,445,511,550.8,587.8,574.1,535.4,591.5

Explanation / Answer

Solution

Back-up Theory

Let Y = ILE and X = DLH

Then, Mean X = Xbar = (1/n)sum of xi over I = 1, 2, …., n; ……………….(1)

Sxx = sum of (xi – Xbar)2 over i = 1, 2, …., n ………………………………..(2)

Similarly, Mean Y = Ybar =(1/n)sum of yiover i= 1, 2, …., n;…………….(3)

Syy = sum of (yi – Ybar)2 over i = 1, 2, …., n ………………………………(4)

Sxy = sum of {(xi– Xbar)(yi– Ybar)} over i = 1, 2, …., n………(5)

Estimated Regression of Y on X is given by: Ycap= a + bX, where

b = Sxy/Sxx and a = Ybar – b.Xbar..…………………….(6)

Physical interpretation of b, also referred as slope, is that per unit change in x, expected (i.e., average) change in y is b……………………………………………..(7)   

Now, to work out solution,

From the given data the following are computed using Excel Function.

n = 18;   Xbar = 26.83;   Ybar = 456.21     Sxy = 7620.80    Sxx = 454.5

b = 16.77    a = 6.28

Part (a)

Straight line fit of regression is: ycap = 6.28 + 16.77x i.e., ILEcap = 6.28 + 16.77DLH   [This is a straight line cutting x-axis at – 0.37 and y-axis at 6.28] ANSWER

Part (b)

[vide (2) under Back-up Theory], if direct labor hours (DLH) increases by one hour, the indirect labor expense (ILE), on average, increases by 16.77. ANSWER

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