Ch E 310 - Fall 10 - Lecture 15

Ch E 310 - Fall 10 - Lecture 15 - Lecture 15 October 14,...

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Lecture 15 – October 14, 2010 Agenda: Linear Regression In-Class Exercise 8: linear_fit.m Pick up Exam 1 (if you want it) HW 3 questions (due tomorrow at noon)
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Stats Review: Mean and Variance For curve fitting, we have to understand how data is sometimes distributed (a model) Mean: average of data points: Span: overall “width” of the data: Variance: deviation of data from the mean: The above is the “unbiased” sample variance n x x n i i 1     i i x x min max 1 2 1 2 n x x n i i x 1 2 1 n x x n i i x
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Stats Review: Mean and Variance Example: test score distributions (normal) Mean tells us something about the class as a whole Variance (or standard deviation) tells us how widely distributed the results were A normal distribution is described using two parameters only
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Stats Review: Mean and Variance MATLAB has built-in statistical functions: >> x = rand(1,6) x = 0.3816 0.7655 0.7952 0.1869 0.4898 0.4456 >> mean(x) ans = 0.5107 >> var(x) ans = 0.0544 >> std(x) ans = 0.2333 >> hist(x)
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Linear Regression: Example Example: Fitting absorbance data Beer’s law: A = a l c a = extinction, l = path length, c = concentration Incoming light is partially absorbed by molecules in the cuvette Absorbance should be directly proportional to concentration of a sample, all else equal I / I 0 = 10 - A A = log 10 ( I 0 / I )
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Linear Regression: Example Based on the form of Beer’s law, we expect a linear relationship between A and c However, we know that experimental error and other uncertainties will lead to there being slight deviations between the linear model predictions and the measured data Our model for the data is: y = ax + b where: y = absorbance, a = a l , b is a constant
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This note was uploaded on 09/21/2011 for the course CH E 310 taught by Professor Staff during the Spring '08 term at Iowa State.

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Ch E 310 - Fall 10 - Lecture 15 - Lecture 15 October 14,...

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