ES240_Chpt13 - ES 240: Scientific and Engineering...

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1 ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression 13. 1: Statistical Review Uchechukwu Ofoegbu Temple University ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression Measure of Location ± Arithmetic mean : the sum of the individual data points ( y i ) divided by the number of points n : ± Median : the midpoint of a group of data. ± Mode : the value that occurs most frequently in a group of data. y = y i n ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression Measures of Spread ± Standard deviation : where S t is the sum of the squares of the data residuals: and n -1 is referred to as the degrees of freedom . ± Sum of squares : ± Variance : s y = S t n 1 S t = y i y () 2 s y 2 = y i y 2 n 1 = y i 2 y i 2 / n n 1 c.v. = s y y × 100% ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression Normal Distribution ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression Descriptive Statistics in MATLAB Descriptive Statistics in MATLAB ± MATLAB has several built-in commands to compute and display descriptive statistics. Assuming some column vector, s : – mean( s ), median( s ), mode( s ) • Calculate the mean, median, and mode of s . mode is a part of the statistics toolbox. –m i n ( s ), max( s ) • Calculate the minimum and maximum value in s . –v a r ( s ), std( s ) • Calculate the variance and standard deviation of s ± Note - if a matrix is given, the statistics will be returned for each column. ES 240: Scientific and Engineering Computation. Chapter 13: Linear Regression Histograms in MATLAB Histograms in MATLAB ± [ n , x ] = hist( s , x ) – Determine the number of elements in each bin of data in s . x is a vector containing the center values of the bins.
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ES240_Chpt13 - ES 240: Scientific and Engineering...

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