A manufacturing company wants to develop a budget to predict how monthly mainten
ID: 3061779 • Letter: A
Question
A manufacturing company wants to develop a budget to predict how monthly maintenance costs vary with activity levels. Management is trying to decide whether hours used or units produced is the better measure of maintenance cost. Monthly data for the preceding 24 months is given below.
Month
Hours
Units
Maintenance
Month
Hours
Units
Maintenance
1
1304
111
30800
13
1301
138
30500
2
1397
114
32900
14
1438
123
34000
3
1465
133
33800
15
1194
124
29000
4
1232
129
29900
16
1355
144
32600
5
1487
147
34200
17
1149
120
28200
6
1223
130
28700
18
1244
120
30000
7
1238
122
29600
19
1158
106
28800
8
1406
119
31600
20
1418
150
33100
9
1179
105
28000
21
1117
121
26700
10
1272
125
30300
22
1340
116
31200
11
1344
126
31600
23
1334
129
30900
12
1324
145
31800
24
1387
150
32700
Use regression to determine which measure, Hours or Units (or both), should be used for the budget.
Your boss asks you to predict the maintenance cost when 1587 Hours are used and 178 Units are produced. Comment on how you would a respond to this prediction request from your boss.
Month
Hours
Units
Maintenance
Month
Hours
Units
Maintenance
1
1304
111
30800
13
1301
138
30500
2
1397
114
32900
14
1438
123
34000
3
1465
133
33800
15
1194
124
29000
4
1232
129
29900
16
1355
144
32600
5
1487
147
34200
17
1149
120
28200
6
1223
130
28700
18
1244
120
30000
7
1238
122
29600
19
1158
106
28800
8
1406
119
31600
20
1418
150
33100
9
1179
105
28000
21
1117
121
26700
10
1272
125
30300
22
1340
116
31200
11
1344
126
31600
23
1334
129
30900
12
1324
145
31800
24
1387
150
32700
Explanation / Answer
Below is given output of R software.
we first run linear regression in R.
Model and summary given below.
> model<-lm(maintaince~hours+unit)
> model
Call:
lm(formula = maintaince ~ hours + unit)
Model is given by
Coefficients:
(Intercept) hours unit
5740.964 18.420 8.685
> summary(model)
Call:
lm(formula = maintaince ~ hours + unit)
Residuals:
Min 1Q Median 3Q Max
-1072.87 -265.81 25.83 313.19 808.17
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5740.964 1334.495 4.302 0.000316 ***
hours 18.420 1.136 16.219 2.36e-13 ***
unit 8.685 9.047 0.960 0.347985
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 489.5 on 21 degrees of freedom
Multiple R-squared: 0.9476, Adjusted R-squared: 0.9426
F-statistic: 189.7 on 2 and 21 DF, p-value: 3.6e-14
Q.1) determine which measure, Hours or Units (or both), should be used for the budget.
I.e. we want to use t test to check significance of variables.
a) for hour
we want to test
Ho:- hour is not significant
V/s
H1:- hour is significant
Here we get direct P value in Coefficient column for unit.
P value = 2.36e-13 < 0.05 (at 95% Level of significance)
Therefore we reject Ho.
Conclusion:- hour is singnificant.
b) for unit
we want to test
Ho:- Unit is not significant
V/s
H1:- Unit is significant
Here we get direct P value in Coefficient column for unit.
P value = 0.347985 > 0.05(at 95% Level of significance)
Therefore we accept Ho.
Conclusion:- Unit is not singnificant.
from a) & b)
Hours should be used for the budget.
Q.2) boss asks you to predict the maintenance cost when 1587 Hours are used and 178 Units are produced.
So we fitted linear regression model above, we use that model to predict the value of maintenance cost .
Our linear regression model is given by,
maintainance= 5740.964+(18.420*hours) + (8.685* unit)
Hours= 1587 , units = 178
Using values in above model.
maintainance = 5740.964 + (18.420*1587) + (8.685* 178)
maintainnance = 36519.43
predicted value of the maintenance cost when 1587 Hours are used and 178 Units are produced is 36519.43
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