3. The data below are a sample of 57 consecutive measurements recorded from a complex machine tool at Deere & Co. The values given are deviations from a target value

in units of ten millionths of an inch. The process employs a control mechanism that resets some of the parameters of the machine tool depending on the magnitude of deviation from the target of the last item produced. The data are available on Carmen. (a) Argue that the series appears to be stationary. Be specific in your arguments. (b) Based on the description of the data above, is it reasonable to consider the data to be independent? Say why or why not. (c) Use the Box-Ljung statistic to test whether the data in the series are independent. Be sure to clearly state the hypotheses you are testing, report the test statistic and its associated p-value, and provide a conclusion in words. Be sure to report the number of lags you include in the calculation of the test statistic. (d) Use R to calculate (h) and p(h), the sample ACVF and ACF, out to a maximum of lag h 7. Make a plot of the estimates and report the numeric values of (h). (e) Estimate u, the mean deviation from target value, and provide an approximate 95% confidence interval for μ. Only include the terms (h) for h = 0,..., [√π] = 7 in the sum when calculating the standard error of as described in class as the sample ACVF can be unreliable for large h. (f) Compare the confidence interval you calculated above to the one you would calcu- late if you assumed the data were independent. Would (incorrectly) assuming the data are independent lead to underconfident or overconfident conclusions about fl based on your calculations? (g) Carefully explain what the blue dotted lines represent in the plot generated by the R function acf. What tentative conclusion might you draw about the true ACF p(h) for the process generating the data? Deviations (ten millionths of an inch) Frequency 0009 2000 -2000 0 -6000 15 J 10 5 0 0 -6000 10 -2000 0 2000 www/w 20 Order of Measurements in Time 6000 Deviations (ten millionths of an inch) 30 X1+1 4000 2000 0 -2000 -6000 40 -6000-4000 -2000 X₂ 0 50 2000 4000/n 18/02/2024, 02:04 -500 - 1250 -500 - 3000 - 2375 2000 2375 1500 -625 250 0 625 3125 2125 2250 3875 1000 250 750 750 -375 -625 -875 - 1125 250 -250 - 125 - 1750 625 125 625 -375 875 -500 250 625 -250 2375 - 2000 125 125 - 1000 375 - 1250 500 1625 1875 1875 3000 3625 750 - 1125 - 2875 -5750 - 1750 - 750 -750 mediatb.blob.core.windows.net/media//65d115933e5c9b9de4d18f6c/questions/deere_deviation_data_170... https://mediatb.blob.core.windows.net/media//65d115933e5c9b9de4d18f6c/questions/deere_deviation_data_1708201561025.txt 1/1