Your boss would like you to estimate the fixed and variable components of a particular cost. Actual data for this cost over four recent periods appear below. Activity Cost
Period 1 32 $388
Period 2 31 $377
Period 3 30 $362
Period 4 35 $406

Using the least-squares regression method, what is the cost formula for this cost?

y =$115.75 + $8.36X

Explanation:

Calculation for what is the cost formula for this cost Using the least-squares regression method

First step is to calculate the Total amount of Period 1 to Period 4

Month Activity(X) Cost(Y) Square of X X*Y

Period 1 32 $388 $1,024 $12,416

Period 2 31 $377 $961 $11,687

Period 3 30 $362$ 900 $10,860

Period 4 35 $406 $1,225 $14,210

TOTAL 128 $1,533 $4,110 $49,173

Second step is to calculate Unit Variable Cost using this formula

Unit Variable Cost = nΣxy − (Σx)(Σy) /nΣx^2 − (Σx)^2

Where,

n =4

Σx =128

Σy =1,533

Σx^2=4,110

Σxy =49,173

Let plug in the formula

Variable cost per unit =4*49,173 - (128*1,533) / 4*4,110 - 128^2

Variable cost per unit=(196,692 - 196,224) / (16,440 - 16,384)

Variable cost per unit= 468 / 56

Variable cost per unit=$8.36

The third step is to calculate Total Fixed Cost

Using this formula

Total Fixed Cost = Σy − bΣx / n

Where,

Σy=1,533

bΣx=$8.36*128

n=4

Let plug in the formula

Total Fixed cost =1,533 - ($8.36*128) / 4

Total Fixed cost =(1,533 - 1,070) / 4

Total Fixed cost =$463 / 4

Total Fixed cost =$115.75

Hence,the cost formula for this cost will be:

Cost formula=Total Fixed cost + Variable cost per unit

y =$115.75 + $8.14X

Therefore Using the least-squares regression method, the cost formula for this cost is y =$115.75 + $8.36X

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