1 / 9

Regression Analysis in Engineering: Interpolation, Curve Fitting, and Predictive Modeling

This lecture focuses on the fundamentals of regression analysis in engineering contexts, emphasizing the distinction between independent and dependent variables. We will explore interpolation techniques to derive values between known data points, curve fitting methods, and the importance of understanding data relationships for prediction tasks. The least squares fit for error minimization will be detailed, along with functional forms such as linear, polynomial, exponential, and others. The lecture will also cover quality assessment of the fit through R-squared values and advanced regression possibilities.

danton
Télécharger la présentation

Regression Analysis in Engineering: Interpolation, Curve Fitting, and Predictive Modeling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EGR 105 Foundations of Engineering I Fall 2007 – week 7 Excel part 3 - regression

  2. Analysis of x-y Data • Independent versus dependent variables y y = f(x)x dependent independent

  3. Finding Other Values • Interpolation • Data between known points • Regression – curve fitting • Simple representation of data • Understand workings of system • Useful for prediction • Extrapolation • Data beyond the measured range data points

  4. Regression • Useful for noisy or uncertain data • n pairs of data (xi , yi) • Choose a functional form y = f(x) • polynomial • exponential • etc. and evaluate parameters for a “close” fit

  5. y (x3,y3) (x4,y4) (x1,y1) (x2,y2) e3 ei= yi – f(xi), i =1,2,…,n x What Does “close” Mean? errors squared sum • Want a consistent rule • Common is the least squares fit (SSE):

  6. y x Quality of the Fit: Notes: is the average y value 0 R2 1 closer to 1 is a “better” fit

  7. Linear Regression • Functional choicey = m x + b slopeintercept • Squared errors sum to • Set m and b derivatives to zero

  8. Further Regression Possibilities: • Could force intercept: y = m x + c • Other two parameter ( a and b ) fits: • Logarithmic: y = a ln x + b • Exponential: y = a e bx • Power function: y = a x b • Other polynomials with more parameters: • Parabola: y = a x2 + bx + c • Higher order: y = a xk + bxk-1 + …

  9. Function Discoveryor How to find the best relationship • Look for straight lines on log axes: àlinear on semilog x y = a ln x + b àlinear on semilog y y = ae bx àlinear on log log y = ax b • No rule for 2nd or higher order polynomial fits (not very useful toward real problems)

More Related