Question

An important application of regression analysis is the estimation of cost, particularly the effect of production volume on total cost. The following data come from a company which has kept track of production volume and total cost at several different levels of production.

Production volume (units)		Total cost ($)
400		4000
450		5000
550		5400
600		5900
700		6400
750		7000

Use these data to estimate a regression designed to capture the effect of production volume on the total cost.

A. What are b₀ and b1? Round your answer to 1 decimal place.
B.Use your regression equation to estimate the total cost when production volume = 500? Round your answer to the dollar (0 decimal places).
C.Use your regression equation to estimate the total cost when production volume = 650? Round your answer to the dollar (0 decimal places).
D.Use your regression equation to estimate the total cost when production volume = 1,000? Round your answer to the dollar (0 decimal places).

Answer 1

Answer to first question :

Let the regression equation :

Y = a + b.X

Y = Total cost

X = Production volume

A, b = constants

We place all the values of X,Y as provided in two adjacent columns in excel and apply the formula LIEST ( ) to obtain values of a, b .

Accordingly :

A = 1246.7

B = 7.6

Thus :

Y = 1246.7 + 7.6.X

Bo = 1246.7     B1 = 7.6

Answer to second question :

Total cost when production volume = 500 ( we put X = 500)

= 1246.7 + 7.6 x 500 =1246.7 + 3800 = 5046.7 ( 5047 rounded to nearest whole number )

Answer to third question :

Total cost when production volume = 650 ( we put X = 650 )

= 1246.7 + 7.6 x 650

= 1246.7 + 4940

= 6186.7 ( 6187 rounded to nearest whole number )

Answer to fourth question :

Total cost when production volume = 1000 ( we put X = 1000)

= 1246.7 + 7.6 x 1000

= 1246.7 + 7600

= 8846.7 ( 8847 rounded to nearest whole number )