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 are given in the file ILE_and_DLH.xlsx 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.

DLH(X) ILE(Y)

20 361

25    400

22    376

23    384

20    361

19    360

24    427.2

28    458.4

26    450.8

29    475.2

27 462.6

25 445

28 511

32 550.8

35 587.8

34 574.1

30 535.4

36 591.5

Answer 1

The following data are passed:

DLH	ILE
20	361
25	400
22	376
23	384
20	361
19	360
24	427.2
28	458.4
26	450.8
29	475.2
27	462.6
25	445
28	511
32	550.8
35	587.8
34	574.1
30	535.4
36	591.5

The independent variable is DLH, and the dependent variable is ILE. In order to compute the regression coefficients, the following table needs to be used:

	DLH	ILE	DLH*ILE	DLH2	ILE2
	20	361	7220	400	130321
	25	400	10000	625	160000
	22	376	8272	484	141376
	23	384	8832	529	147456
	20	361	7220	400	130321
	19	360	6840	361	129600
	24	427.2	10252.8	576	182499.84
	28	458.4	12835.2	784	210130.56
	26	450.8	11720.8	676	203220.64
	29	475.2	13780.8	841	225815.04
	27	462.6	12490.2	729	213998.76
	25	445	11125	625	198025
	28	511	14308	784	261121
	32	550.8	17625.6	1024	303380.64
	35	587.8	20573	1225	345508.84
	34	574.1	19519.4	1156	329590.81
	30	535.4	16062	900	286653.16
	36	591.5	21294	1296	349872.25
Sum =	483	8311.8	229970.8	13415	3948890.54

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

ILE = 52.182 + 15.264 * DLH

i.e.

y = 52.182 + 15.264 * x

Graphically:

When DLH increases by 1 hour then ILE increases by approx:

ILE = 52.182 + 15.264 * 1 = 67.446 ~ 67.45

Please upvote. Thanks!