Correlation (Pearson, Kendall, Spearman)

A comparison of the Pearson and Spearman correlation methods

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# Category: Math

## Correlation (Pearson, Kendall, Spearman)

## Hypothesis Testing

## Cyclismo Online R Tutorials

## Linear Least Squares Regression

## NIST Digital Library of Mathematical Functions

## Engineering and Statistics Handbook

## Special Products in Sage

Primers from Stattrek.com

– Hypothesis Tests Intro

– Hypothesis Tests Effect Size and Factors

– Hypothesis Tests Procedure

KhanAcademy Inferential Statistics

– Hypothesis Testing w/ one sample

— Normal distribution

— Z-scores

— Empirical rule

— Sampling distribution of sample mean

– Hypothesis Testing w/ two samples

Jason Delaney Playlists

– Hypothesis testing – one population – mean or proportion

– Hypothesis testing – 2 populations – means or proportions

Inference for Variances (Jason Delaney)

Great tutorial for learning R, completely free and online.

Jason Delany: Simple Linear Regression YouTube Playlist

Khan Academy Least Squares Videos

– Least squares approximation

– Least squares examples

– Uses matrices and linear algebra

— Matrix equations

— Matrices for solving systems of eqns

– Linear Regression & Correlation

Dawn E. Wright, Ph.D. posted a list of regression related video links.

The U.S. National Institute of Standards and Technology (NIST) have a killer resource for all math functions organized by discipline.

NIST and Sematech published an comprehensive free e-book on statistical modeling analysis and how to apply it to engineering and scientific work.

The Case Studies chapters in each of the sections are of special usefulness.

Initializing Variables:

sage: a,b,c,d,x = var('a,b,c,d,x')

Product of a Monomial and a Binomial

sage: eqn_mon_bin = a*(c+d) sage: eqn_mon_bin.expand() a*c + a*d

Product of the Sum and the Difference of Two Terms

sage: eqn_prod_sum_diff = (a+b)*(a-b) sage: eqn_prod_sum_diff.expand() a^2 - b^2

Square of a Binomial

sage: eqn_bin_sq = (a+b)^2 sage: eqn_bin_sq.expand() a^2 + 2*a*b + b^2 sage: eqn_bin_sq_diff = (a-b)^2 sage: eqn_bin_sq_diff.expand() a^2 - 2*a*b + b^2

Product of Two Binomials

sage: eqn_bin_prod = (x+a)*(x+b) sage: eqn_bin_prod.expand() a*b + a*x + b*x + x^2

Cube of Binomial

sage: eqn_bin_cube = (a+b)^3 sage: eqn_bin_cube.expand() a^3 + 3*a^2*b + 3*a*b^2 + b^3

Square of a Trinomial

sage: eqn_tri_sq = (a+b+c)^2 sage: eqn_tri_sq.expand() a^2 + 2*a*b + b^2 + 2*a*c + 2*b*c + c^2

Tools:

1. SageMathCloud

References:

1. Sage Docs – Symbolic Expressions

2. Schaum’s Outline of College Algebra