Answer:
a. y = 1246.667 + 7.6x
b $7.6 per unit
Explanation:
a..
Given
n = 6.
Solving the regression equation using
y = a + bx
See attachment for solution
a = 1246.667
b = 7.3
So, y = 1246.667 + 7.3x
b.
The Variable cost per unit is given by the slope of the regression equation i.e. the coefficient of x
Which is 7.6
Answer:
Regression equation: Y = 1,246.67 + 7.6X
Variable cost per unit = $7.6
Explanation:
The regression equation will be in the form [tex]Y = a + bX[/tex]
Where Y = total cost,
X = production volume,
a = constant, i.e. total cost when production volume = 0,
b = variable cost.
"b" and "a" can be computed as follows:
[tex]b = \frac{NEXY - EXEY}{NEX^{2} - (EX)^{2} }[/tex] (letter "E" was used in the place of summation)
[tex]a = \frac{EY - bEX}{N}[/tex]
The computation of the variables in the above equation are done in the file attached.
thus [tex]b = \frac{(6*20,090,000) - (3,450*33,700)}{(6*2,077,500) - (3,450)^{2} }[/tex]
= [tex]\frac{120,540,000 - 116,265,000}{12,465,000 - 11,902,500}\\[/tex]
= 7.6
and
[tex]a = \frac{33,700-(7.6*3,450)}{6}[/tex]
= 1,246.67.
Therefore, the regression equation is Y = 1,246.67 + 7.6X.
Variable cost per unit produced is "b" = $7.6.
