Calculate Statistically Whether or Not Machines Need to be Replaced or Repaired

Question

The production manager 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 are becoming quite unreliable.  However, the cost of replacing them is quite high and the manager is not certain that the cost can be recouped given the 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.  This data are stored in the Excel sheet attached.

Answer the following questions:

a)    Obtain a scatter diagram using the data and describe the relationship you observed.
b)    Estimate the relationship between the two variables and interpret the coefficients.
c)    Conduct a test at whatever significance level you deem suitable to determine whether the age of a machine and its monthly cost of repair are linearly related.
d)    Interpret the coefficient of determination.
e)    Do you think the relationship you have estimated is good enough for the production manager to use to forecast for a machine that is 95 months old?  180 months old?  Explain your answers.

Summary

These questions belong to Statistics and it is about a car seat manufacturer who wants to know whether it is economical to replace the machines or to get them repaired. Various questions such as scatter diagram, coefficient interpretation, correlation coefficient, etc have been answered in the solution in detail.

Total Word Count 291

 

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