A cost accountant has derived the following data on the weekly output of standard size boxes...

A cost accountant has derived the following data on the weekly output of standard size boxes from a factory.

Week	Output (thousands)	Total cost (thousand dollars)
1	20	60
2	2	25
3	4	26
4	23	66
5	18	49
6	14	48
7	10	35
8	8	18
9	13	40

(a) Determine the regression equation from which we can predict the total cost in terms of the weekly production. (4%)

(b) In the following week it is planned to produce 15,000 standard size boxes. Estimate the total cost of producing this quantity. (1%)

(c) Compute the linear correlation coefficient. Interpret the result.

Expert Solution

Week	Output (thousands) X	Total cost (thousand dollars) Y	*XY**	X^2	Y^2
1	20	60	1200	400	3600
2	2	25	50	4	625
3	4	26	104	16	676
4	23	66	1518	529	4356
5	18	49	882	324	2401
6	14	48	672	196	2304
7	10	35	350	100	1225
8	8	18	144	64	324
9	13	40	520	169	1600
Sum	112	367	5440	1802	17111

Regression equation=> Y’=a+bX

Where = = 2.138

= = 14.168

Regression equation Y’= 14.168+2.318X

b) For 15000 units the total cost is y= 11.93+(2.318*15000) = 34781.9

c) Correlation coefficient=

Correlation coefficient= 0.93

The relation between output and cost are strongly related because the correlation is greater than 0.75

jeff jeffy answered 1 year ago

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