Homework 5 Solution

Homework 5 Solution - MEEN 260 Introduction to Engineering...

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MEEN 260 Introduction to Engineering Experimentation Homework 5: Regression and Strain Gauges Assigned: Thursday, 14 Feb. 2008 Due: Thursday, 21 Feb. 2008, 9:00am Homework Problems: Problem 1) Consider the data set given below: Measurement x y 1 0.1 5.5 2 0.3 7.4 3 0.6 9.1 4 1.2 16.4 5 1.5 22.1 6 1.6 24.4 7 1.7 26.9 8 1.9 32.8 Develop the least-squares fit to the following data using a linear regression b ax y + = , a 2 nd order regression 2 1 y ax = + , and an exponential regression ax Ce y = . a) Determine the coefficients for all three regression models based on the summation formulas provided in the lecture notes. Derive your own summation formulas if necessary. Don’t use built-in functions of Excel to get the regressions directly; but you may use Excel to do the summations, generate the plots, etc. b) Determine the coefficients for all three regression models based on the matrix formulation of regression as presented in the lecture notes. You may use Matlab, Maple or similar software to do the matrix inversion, but show the values for all matrices and vectors in your homework. c) Do the coefficients obtained from both methods agree? (If they don’t, you’ve made a mistake)
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