Total production cost each week in a production department have been measured for the past five...

Total production cost each week in a production department have been measured for the past five weeks as follows:

Week	Units Produced	Total Cost (GH₵)
1	5	20000
2	9	27000
3	4	17000
4	5	19000
5	6	23000

Required:

a. Use linear regression analysis to obtain an estimate of the fixed cost per week and the variable cost of production per unit.

b. Use your results to estimate the total cost in a week when 8 units are produced.

c. Calculate the correlation coefficient and comment on the value of r that you have obtained. (2marks)

d. Estimate a value for fixed costs and variable costs from the same data, using the high/low analysis and use the values that you have obtained to estimate the total costs in a week when 8 units are produced.

Expert Solution

a)
SUMMARY OUTPUT

Regression Statistics
Multiple R	0.97341986
R Square	0.94754623
Adjusted R Square	0.93006164
Standard Error	1031.0495
Observations	5

ANOVA
	df	SS	MS	F	Significance F
Regression	1	57610810.8	57610810.8	54.1932203	0.0051812
Residual	3	3189189.19	1063063.06
Total	4	60800000

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9756.75676	1621.39638	6.01750249	0.00919699	4596.74984	14916.7637	4596.74984	14916.7637
X Variable 1	1972.97297	268.008555	7.36160447	0.0051812	1120.05014	2825.89581	1120.05014	2825.89581

Fixed Cost	9756.76
Variable cost per unit	1972.97
Y = 9756.76 + 1972.97 X

b)
Total cost in week = 9756.76 + 1972.97 x 8 units	25540.54

c)
Correlation coefficient = Multiple R	0.97
Units produced and total cost relationship is a positive correlation coefficient.

d)
Units Produced	Total Cost (GH₵)
5	20000
9	27000
4	17000
5	19000
6	23000

Variable cost per unit = (Highest Activity Cost - Lowest Activity Cost)/(Highest Activity Units - Lowest Activity Units)
Variable cost per unit = (27000 - 23000)/(9-6)units	$ 1,333.33
Fixed cost = Highest Activity Cost - (Variable Cost Per Units x Highest Activity Units)
Fixed cost = 27000 - (1333.33 x 9 units)	$ 15,000.00
Y = $15000 + $1,333.33 x 8 units	$ 25,666.67

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