An accountant wishes to predict direct labor cost ( y ) on the basis of the batc
ID: 3388466 • Letter: A
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.
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 LaborCost, 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
Explanation / Answer
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