Regression Analysis. Unscheduled Maintenance Issue: l 36 flight squadrons l Each experiences unscheduled maintenance actions (UMAs) l UMAs costs $1000.
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Presentation on theme: "Regression Analysis. Unscheduled Maintenance Issue: l 36 flight squadrons l Each experiences unscheduled maintenance actions (UMAs) l UMAs costs $1000."— Presentation transcript:
95% Confidence Interval on our estimate of UMAs and costs l 60 + 2(2) = [56, 64] l low cost: 56 * $1000 * 36 = $2,016,000 l high cost: 64 * $1000 * 36 = $2,304,000
What do you want to know? l How many UMAs will there be next month? l What is the average number of UMAs ? l Is there a relationship between UMAs and and some other variable that may be used to predict UMAs? l What is that relationship?
Relationships l What might be related to UMAs? n Pilot Experience ? n Flight hours ? n Sorties flown ? n Mean time to failure (for specific parts) ? n Number of landings / takeoffs ?
Regression: l To estimate the expected or mean value of UMAs for next month: n look for a linear relationship between UMAs and a “predictive” variable n 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? l quantifiable l predictable l logical relationship with dependent variable l must be a linear relationship: Y = a + bX
Describing the Relationship l Is there a relationship? n Do the two variables (UMAs and sorties or experience) move together? n Do they move in the same direction or in opposite directions? l How strong is the relationship? n How closely do they move together?
Correlation Coefficient l Statistical measure of how closely two variables are moving together in a coordinated fashion n Measures strength and direction l Value ranges from -1.0 to +1.0 n +1.0 indicates “perfect” positive linear relation n -1.0 indicates “perfect” negative linear relation n 0 indicates no relation between the two variables
A Word of Caution... l Correlation does NOT imply causation n It simply measures the coordinated movement of two variables l Variation in two variables may be due to a third common variable l The observed relationship may be due to chance alone
What is the Relationship? l In order to use the correlation information to help describe the relationship between two variables we need a model l The simplest one is a linear model:
Testing Model Parameters l How well does the model explain the variation in the dependent variable? l Does the independent variable really seem to matter? l Is the intercept constant statistically significant?
Basic Steps of Regression Analysis l Formulate the model l Plot scatter diagram for visual inspection l Compute correlation coefficient l Fit the regression line l Test the model
Factors affecting estimation accuracy l Sample size (larger is better) l Range of X values (wider is better) l Standard deviation of U (smaller is better)
Uses and Limitations of Regression Analysis l Identifying relationships n Not necessarily cause n May be due to chance only l Forecasting future outcomes n Only valid over the range of the data n Past may not be good predictor of future
Common pitfalls in regression l Failure to draw scatter diagrams l Omitting important variables from the model l The “two point” phenomenon l Unfounded claims of model sophistication l Insufficient attention to interval estimates and predictions l Predicting too far outside of known range
Summary l Regression Analysis is a useful tool n Helps quantify relationships l But be careful n Does not imply cause and effect n Don’t go outside range of data n Check linearity assumptions n Use common sense!
Non-linear relationship between output and cost