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Regression Analysis. Defense Resources Management Institute. Unscheduled Maintenance Issue:. 36 flight squadrons Each experiences unscheduled maintenance actions (UMAs) UMAs costs $1000 to repair, on average. You’ve got the Data… Now What?. Unscheduled Maintenance Actions (UMAs).

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## Regression Analysis

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**Regression Analysis**Defense Resources Management Institute**Unscheduled Maintenance Issue:**• 36 flight squadrons • Each experiences unscheduled maintenance actions (UMAs) • UMAs costs $1000 to repair, on average.**You’ve got the Data… Now What?**Unscheduled Maintenance Actions (UMAs)**What do you want to know?**• How many UMAs will there be next month? • What is the average number of UMAs ?**UMAs Next Month**95% Confidence Interval**Average UMAs**95% Confidence Interval**Model: Cost of UMAs for one squadron**If the cost per UMA = $1000, the Expected cost for one squadron = $60,000**Model: Total Cost of UMAs**Expected Cost for all squadrons = 60 * $1000 * 36 = $2,160,000**Model: Total Cost of UMAs**Expected Cost for all squadrons = 60 * $1000 * 36 = $2,160,000 How confident are we about this estimate?**~ 95%**mean (=60) standard error =12/36 = 2**~56 ~58 60 ~62 ~64**(1 standard unit = 2) ~ 95%**95% Confidence Interval on our estimate of UMAs and costs**• 60 + 2(2) = [56, 64] • low cost: 56 * $1000 * 36 = $2,016,000 • high cost: 64 * $1000 * 36 = $2,304,000**What do you want to know?**• How many UMAs will there be next month? • What is the average number of UMAs ? • Is there a relationship between UMAs and and some other variable that may be used to predict UMAs? • What is that relationship?**Relationships**• What might be related to UMAs? • Pilot Experience ? • Flight hours ? • Sorties flown ? • Mean time to failure (for specific parts) ? • Number of landings / takeoffs ?**Regression:**• To estimate the expected or mean value of UMAs for next month: • look for a linear relationship between UMAs and a “predictive” variable • If a linear relationship exists, use regression analysis**Regression analysis:**describes and evaluates relationships between one variable (dependent or explained variable), and one or more other variables (called the independent or explanatory variables).**What is a good estimating variable for UMAs?**• quantifiable • predictable • logical relationship with dependent variable • must be a linear relationship: Y = a + bX**Describing the Relationship**• Is there a relationship? • Do the two variables (UMAs and sorties or experience) move together? • Do they move in the same direction or in opposite directions? • How strong is the relationship? • How closely do they move together?**Correlation Coefficient**• Statistical measure of how closely two variables are moving together in a coordinated fashion • Measures strength and direction • Value ranges from -1.0 to +1.0 • +1.0 indicates “perfect” positive linear relation • -1.0 indicates “perfect” negative linear relation • 0 indicates no relation between the two variables**Sorties vs. UMAs**r = .9788**Experience vs. UMAs**r = .1896**A Word of Caution...**• Correlation does NOT imply causation • It simply measures the coordinated movement of two variables • Variation in two variables may be due to a third common variable • The observed relationship may be due to chance alone**What is the Relationship?**• In order to use the correlation information to help describe the relationship between two variables we need a model • The simplest one is a linear model:**One Possibility**Sum of errors = 0**Another Possibility**Sum of errors = 0**Which is Better?**• Both have sum of errors = 0 • Compare sum of absolute errors:**One Possibility**Sum of absolute errors = 6**Another Possibility**Sum of absolute errors = 6**Which is Better?**• Sum of the absolute errors are equal • Compare sum of errors squared:**The Correct Relationship: Y = a + bX + U**Y systematic random 100 90 80 70 60 50 X 100 110 120 130**The correct relationship:**• Y = a + bX + U Y systematic random 100 90 80 70 60 50 X 100 110 120 130**Least-Squares Method**• Penalizes large absolute errors • Y- intercept: • Slope:**Assumptions**• Linear relationship: • Errors are random and normally distributed with mean = 0 and variance = • Supported by Central Limit Theorem

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