Sample Regression Line

16.100    Xr16-100 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 and the ages (in months) of the   plant’s 20 welding machines.   

• a. Find   the sample regression line.  

 • b.   Interpret the coefficients.   

• c.   Determine the coefficient of determination, and discuss what this statistic   tells you.  

 • d. Conduct   a test to determine whether the age of a machine and its monthly cost of   repair are linearly related.   

• e. Is the   fit of the simple linear model good enough to allow the president to predict   the monthly repair cost of a welding machine that is 120 months old? If so,   find a 95% prediction interval. If not, explain why not.          

 Age Repairs   110 327.67   113 376.68   114 392.52   134 443.14   93 342.62   141 476.16   115 324.74   115 338.98   115 433.45   142 526.37   96 362.42   139 448.76   89 335.27   93 350.94   91 291.81   109 467.8   138 474.48   83 354.15   100 420.11   137 416.04    

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