An accountant wishes to predict direct labor cost y on the b

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.

  

  
bad media

Find b₁ and b₀. (Round your intermediate value and final answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)

  

  b₁ is the estimated

in for every 1 unit increase in
  

.

  b₀ is the estimated

when = 0;

.

Write the least squares prediction equation. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)

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.)

Direct Labor Cost Data
Direct Labor Cost, y ($100s)	Batch Size, x
	625			14
	700			17
	559			28
	313			18
	922			55
	571			79
	432			58
	852			91
	462			66
	764			78
	235			33
	167			58

Solution

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

625

14

700

17

559

28

313

18

922

55

571

79

432

58

852

91

462

66

764

78

235

33

167

58

  

Regression Analysis

r²

0.085

n

12

r

0.291

k

1

Std. Error

239.678

Dep. Var.

cost(y)

ANOVA table

Source

SS

df

MS

F

p-value

Regression

53,328.3047

1  

53,328.3047

0.93

.3580

Residual

574,453.3620

10   

57,445.3362

Total

627,781.6667

11  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=10)

p-value

95% lower

95% upper

Intercept

421.2999

150.5849

2.798

.0189

85.7759

756.8240

size(x)

2.5990

2.6975

0.963

.3580

-3.4113

8.6093

Predicted values for: cost(y)

95% Confidence Interval

95% Prediction Interval

size(x)

Predicted

lower

upper

lower

upper

Leverage

60

577.240

410.849

743.630

17.884

1,136.595

0.097

(a)

Find b₁ and b₀. (Round your intermediate value and final answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)

  

  b₁   = 2.5990

  b₀ = 421.2999

(b)

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

  b₁ is the estimated

in for every 1 unit increase in size, the increase in cost(in 100s)
  

.

  b₀ is the estimated

when size x = 0;

No, the interpretation of b₀ make no practical sense

.

(c)

Write the least squares prediction equation. (Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.)

   Y = 421.2999 + 2.5990 x

(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.)

   y(60) = 577.240 hundreds of dollars.

Direct Labor Cost Data
Direct Labor Cost, y ($100s)	Batch Size, x
	625			14
	700			17
	559			28
	313			18
	922			55
	571			79
	432			58
	852			91
	462			66
	764			78
	235			33
	167			58