Question

An accountant wishes to predict direct labor cost (y) on the basis of the batch size (x) of a product produced in a job shop. Data for 12 production runs are given in the table below, along with the Excel output from fitting a least squares regression line to the data.

Direct Labor Cost Data
Direct Labor Cost, y ($100s)			Batch Size, x
	71			5
	663			62
	381			35
	138			12
	861			83
	145			14
	493			46
	548			52
	251			23
	1024			100
	435			41
	772			75

  Click here for the Excel Data File

(a) Calculate b₁ and b₀. (Round intermediate steps to 4 decimals places.)

(b) Interpret the meanings of b₀ and b₁. Does the interpretation of b₀ make practical sense?

(c) Write the least squares prediction equation. (Round your answers to 4 decimal places.)

(d) Use the least squares line to obtain a point estimate of the mean direct labor cost for all batches of size 60 and a point prediction of the direct labor cost for an individual batch of size 60. (Round your answer to 3 decimal places.)

Answer 1

a] b1= 10.1463

b0= 18.4875

b] y(hat)= 18.4875+ 10.1463* x

For a unit change in x there will be an increase of 10.1463 unit in dependent variable.

Intercept interpretation: When x= 0 the predicted y will be 10.1463

Intercept interpretation: Since here x=0 then it is saying predicted y will be 10.1463 which is meaningless.

c] y(hat)= 18.4875+ 10.1463* x

d] x=60

y(hat)= 18.4875+ 10.1463* 60

y(hat)= 627.2655