# 14 - Descriptive statistics Least squares Nonlinear...

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Unformatted text preview: Descriptive statistics Least squares Nonlinear relationships Linear Regression Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Linear Regression MATH 2070U 1 / 19 Descriptive statistics Least squares Nonlinear relationships Linear Regression 1 Review of descriptive statistics 2 Linear least-squares regression 3 Linearisation of nonlinear relationships c D. Aruliah (UOIT) Linear Regression MATH 2070U 2 / 19 Descriptive statistics Least squares Nonlinear relationships Descriptive statistics mean y : = 1 n n k = 1 y k mean(y) median y n /2 (after sorting) median(y) mode (most frequent y k ) mode(y) minimum y 1 (after sorting) min(y) maximum y n (after sorting) max(y) variance s 2 y : = S t / ( n- 1 ) var(y) standard deviation s y : = q S t / ( n- 1 ) std(y) histogram visualisation of distribution hist(y,x) S t : = n k = 1 ( y k- y ) 2 = residual sum of squares c D. Aruliah (UOIT) Linear Regression MATH 2070U 4 / 19 Descriptive statistics Least squares Nonlinear relationships Remarks Mode more useful for discrete observations (not continuous) One-pass formula for variance/standard deviation: s 2 y = 1 n- 1 n k = 1 y 2 k- 1 n " n = 1 y #! Not identical in floating-point arithmetic! Normalised measure of spread: coefficient of variation: c.v. : = s y y 100% c D. Aruliah (UOIT) Linear Regression MATH 2070U 5 / 19 Descriptive statistics Least squares Nonlinear relationships Data approximation problem Data approximation problem Given n data points { ( x 1 , y 1 ) , ( x 2 , y 2 ) , . . . , ( x n , y n ) } , determine a function e f that approximates the data, i.e., e f ( x k ) y k ( k = 1: n ) ....
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## This note was uploaded on 06/20/2011 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Winter '10 term at UOIT.

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14 - Descriptive statistics Least squares Nonlinear...

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The provided text appears to be a set of lecture slides or notes on descriptive statistics, least squares, and linear regression, with a focus on mathematical concepts and formulas.
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the text does not contain any explicit mathematical questions or problems to solve. it is primarily a presentation of concepts and formulas related to descriptive statistics and linear regression.
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# 14 - Descriptive statistics Least squares Nonlinear...

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Unformatted text preview: Descriptive statistics Least squares Nonlinear relationships Linear Regression Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Linear Regression MATH 2070U 1 / 19 Descriptive statistics Least squares Nonlinear relationships Linear Regression 1 Review of descriptive statistics 2 Linear least-squares regression 3 Linearisation of nonlinear relationships c D. Aruliah (UOIT) Linear Regression MATH 2070U 2 / 19 Descriptive statistics Least squares Nonlinear relationships Descriptive statistics mean y : = 1 n n k = 1 y k mean(y) median y n /2 (after sorting) median(y) mode (most frequent y k ) mode(y) minimum y 1 (after sorting) min(y) maximum y n (after sorting) max(y) variance s 2 y : = S t / ( n- 1 ) var(y) standard deviation s y : = q S t / ( n- 1 ) std(y) histogram visualisation of distribution hist(y,x) S t : = n k = 1 ( y k- y ) 2 = residual sum of squares c D. Aruliah (UOIT) Linear Regression MATH 2070U 4 / 19 Descriptive statistics Least squares Nonlinear relationships Remarks Mode more useful for discrete observations (not continuous) One-pass formula for variance/standard deviation: s 2 y = 1 n- 1 n k = 1 y 2 k- 1 n " n = 1 y #! Not identical in floating-point arithmetic! Normalised measure of spread: coefficient of variation: c.v. : = s y y 100% c D. Aruliah (UOIT) Linear Regression MATH 2070U 5 / 19 Descriptive statistics Least squares Nonlinear relationships Data approximation problem Data approximation problem Given n data points { ( x 1 , y 1 ) , ( x 2 , y 2 ) , . . . , ( x n , y n ) } , determine a function e f that approximates the data, i.e., e f ( x k ) y k ( k = 1: n ) ....
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## This note was uploaded on 06/20/2011 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Winter '10 term at UOIT.

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14 - Descriptive statistics Least squares Nonlinear...

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The provided text appears to be a set of lecture slides or notes on descriptive statistics, least squares, and linear regression, with a focus on mathematical concepts and formulas.

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The text does not contain any explicit mathematical questions or problems to solve. It is primarily a presentation of concepts and formulas related to descriptive statistics and linear regression.