Lect20 - Detecting Nonlinear Patterns Transformations...

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Detecting Nonlinear Patterns Transformations Reciprocal Transformation Outline Detecting Nonlinear Patterns Transformations Reciprocal Transformation Comparing Linear and Nonlinear Equations Logarithm Transformation 1 / 18 ISOM 2500 Lect 20: Curved Patterns
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Detecting Nonlinear Patterns Transformations Reciprocal Transformation Mileage vs Weight What improvement in mileage should a manufacturer expect from reducing the weight of a car? To answer the question above, we shall use regression analysis to find an equation that summarizes the association between gas mileage and weight 2 / 18 ISOM 2500 Lect 20: Curved Patterns
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Detecting Nonlinear Patterns Transformations Reciprocal Transformation Fitting a Line to the Data Let’s first use the LS linear regression: one gets MPG = 38 . 2 - 5 . 18 * Weight (000 lbs) The equation estimates that mileage would increase = 1.036 MPG, on average, by reducing car weight by 200 pounds. Examining the residuals reveals a clear curved pattern: the residuals are generally positive on the left (light cars), negative in the middle, and positive on the right (heavy cars) 3 / 18 ISOM 2500 Lect 20: Curved Patterns
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Detecting Nonlinear Patterns Transformations Reciprocal Transformation Detecting Nonlinear Patterns Both the scatterplot and residual plot show curved patterns LS linear regression uses a line to describe the relationship between the predictor and the response, and so is not suitable when dealing with curved patterns To recognize nonlinearity, other than looking at the scatterplot, one can also ask the following question: Will changes in the predictor result in equal sized changes in the estimated response, regardless of the value of x? In the mileage case, this amounts to ask Does trimming 200 pounds from a large SUV have the same effect on mileage as trimming 200 pounds from a small compact? If the answer to the above question is “Yes”, then linear regression is probably suitable; otherwise probably some transformations are needed 4 / 18 ISOM 2500 Lect 20: Curved Patterns
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Detecting Nonlinear Patterns Transformations Reciprocal Transformation Transformations
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