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) Construct a scatterplot of the data. Comment on the plot.
(b) Find the correlation coefficient between the repair cost and the machine age.
(c) Find the equation of the regression line for predicting the repair cost from the machine age. (d) Interpret carefully the regression coefficients.
(e) At 5% significance level, test whether the age of a machine and its monthly repair cost are linearly related. (f) Determine the coefficient of determination, and discuss what this statistic tells you.
(g) Obtain the residuals and check the regression assumptions.
(h) Predict the monthly repair cost of a welding machine that is 120 months old.
(i) Predict with 95% confidence the monthly repair cost of a welding machine that is 120 months old.
(j) Predict with 95% confidence the average monthly repair cost of welding machines that are 10 years old.
(k) Predict the monthly repair cost of a welding machine that is 15 years old. Comment on how accurate you feel this prediction is.