14 - Descriptive statistics Least squares Nonlinear...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ) ....
View Full Document

This note was uploaded on 06/20/2011 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Winter '10 term at UOIT.

Page1 / 16

14 - Descriptive statistics Least squares Nonlinear...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online