In: Statistics and Probability
The 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 |
a) Find the coefficient of determination and discuss what this statistic tells you.
b) At 5% significance level, test to determine whether the age of a machine and its monthly cost of repair are linearly related.
c) Predict the average monthly repair cost of welding machines that are 120 months old.
d) Predict with 95% confidence the monthly repair cost of a welding machine that is 120 months old.