Question

he president of a company that manufactures car seats has been concerned about the number and cost of machine breakdowns. The problem is that the machines are old and becoming quite unreliable. However, the cost of replacing them is quite high, and the president is not certain that the cost can be made up in today’s slow economy. To help make a decision about replacement, he gathered data about last month’s costs for repairs in dollars (y) and the ages in months (x) of the plant’s 20 welding machines as recorded :

Ages X	Cost Y
110	655.34
113	753.36
114	785.04
134	886.28
93	685.24
141	952.32
115	649.48
115	677.96
115	866.9
142	1052.74
96	724.84
139	897.52
89	670.54
93	701.88
91	583.62
109	935.6
138	948.96
83	708.3
100	840.22
137	832.08

) At 5% significance level, test to determine whether the age of a machine and its monthly cost of repair are linearly related.

f) Predict the average monthly repair cost of welding machines that are 120 months old.

g) Predict with 95% confidence the monthly repair cost of a welding machine that is 120 months old.

Answer 1

1)
Regression Analysis: Cost Y versus Ages X

The regression equation is
Cost Y = 229.7 + 4.947 Ages X

S = 86.6370 R-Sq = 56.6% R-Sq(adj) = 54.2%

Analysis of Variance

Source DF SS MS F P
Regression 1 176097 176097 23.46 0.000
Error 18 135107 7506
Total 19 311204

2)

welding machines that are 120 months old.

Cost Y = 229.7 + 4.947 Ages X

Cost Y = 229.7 + 4.947 *120

Cost Y = 823.34