Question

2 a) A production manager concerned about the relationship of machine hours and indirect labour cost. Estimate the following data to help manager the unit properly in future. The results are as shown below.

Week	Machine Hour	Indirect Labour (cost)
1	68	1190
2	88	1211
3	62	1004
4	72	917
5	60	770
6	96	1456
7	78	1180
8	46	710
9	82	1316
10	94	1032
11	68	752
12	48	963

            Required: Using least square method;

1. Establish the regression function for the manager.  
2. Using the functions determine the indirect labour cost at 35 units and 90 units of machine hours.                            

Answer 1

Machine Hours	R & M Cost
X	Y	XY	X^2 = X * X
68	1190	80920	4,624
88	1211	106568	7,744
62	1004	62248	3,844
72	917	66024	5,184
60	770	46200	3,600
96	1456	139776	9,216
78	1180	92040	6,084
46	710	32660	2,116
82	1316	107912	6,724
94	1032	97008	8,836
68	752	51136	4,624
48	963	46224	2,304
862	12,501	9,28,716	64,900
X bar = Total Machine Hours/ Total months
X bar =862/ 12	71.83333333
y bar = Total R & M Cost / Total Months
Y bar = $12501/12	1041.75
Cost Equation = a + b x Machine hours
b = (NΣxy − Σx Σy)/N(Σx^2) − (Σx^2
b = (12 x 928716 − 862 x 12501 )/(12 x 64900)- 862^2)	$                     10.31
a = y bar - b x Xbar
a = 1041.75 - (10.31 x 71.83)	$                   300.98
Cost Equation = 300.98 + 10.31 x MH
Labour Cost = 300.98 + 10.31x 35units	$                   661.91
Labour Cost = 300.98 + 10.31x 90 units	$                1,537.58