From 0d9fdc08f809d6445b12309e53143f1f5a8e0af2 Mon Sep 17 00:00:00 2001 From: Paulo Hernane Date: Tue, 22 Aug 2023 08:39:43 -0300 Subject: [PATCH] day 8 of 100 days of code --- blog/2023-08-21-day-8-100-days-of-code.md | 14 +++++ my-brain/data-science/correlation.md | 67 ++++++++++++++++++++++ my-brain/data-science/image.png | Bin 0 -> 129010 bytes 3 files changed, 81 insertions(+) create mode 100644 blog/2023-08-21-day-8-100-days-of-code.md create mode 100644 my-brain/data-science/correlation.md create mode 100644 my-brain/data-science/image.png diff --git a/blog/2023-08-21-day-8-100-days-of-code.md b/blog/2023-08-21-day-8-100-days-of-code.md new file mode 100644 index 00000000..4ab6f706 --- /dev/null +++ b/blog/2023-08-21-day-8-100-days-of-code.md @@ -0,0 +1,14 @@ +--- +slug: day-8-100-days-of-code +title: Day 8 of 100 Days of Code +description: +image: https://github.com/rickmff/100DiasDeCodigo-landing/blob/master/public/thumb.png +authors: paulohfs +tags: [100DaysOfCode, ] +--- + +Today I had a Data Science class and I learned about correlation.You can see my notes [here](https://www.paulohernane.me/my-brain/data-science/correlation), they are incomplete but at the end of this week I will complete them whem reviewing the content to work on a dataset that I had to finish until thursday. + +After that I had some mentorship about distributed systems and some projects to build to improve my skills, I will post my note soon. + +Want to know about the 100 Days of Code Challenge? Check it out [here](https://www.100daysofcode.com/). [PT-BR]() diff --git a/my-brain/data-science/correlation.md b/my-brain/data-science/correlation.md new file mode 100644 index 00000000..c7ce5951 --- /dev/null +++ b/my-brain/data-science/correlation.md @@ -0,0 +1,67 @@ +--- +id: correlation +title: Correlation +tags: + - Data Science + - Statistics + - Correlation +--- + +# Correlation (or Dependence) + +> WORK IN PROGRESS + +Correlation is a statistical measure that describes the interdependence of two or more variables. It is a measure of how close two variables are to having a linear relationship with each other. The closer the correlation value is to -1 or 1, the stronger the relationship between the variables. The closer the correlation value is to 0, the weaker the relationship between the variables. + +## Warning + + Correlation not imply causation. + +Take a look in this graph: + +![Alt text](image.png) + +The graph shows a strong correlation but it's obvious that it is a coincidence. The correlation is not a proof of causation. + +## Covariance + +Before look at how to calculate the correlation, we need to understand about covariance. + +Covariance is a measure of the joint variability of two random variables. It is a measure of how changes in one variable are associated with changes in a second variable. It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together. + +## Pearson Correlation Coefficient + +The Pearson correlation is commonly used in linear correlations. It is a measure of the linear correlation between two variables X and Y. It has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation. + +$$ + pX,Y = CORR(X, Y) = \frac{COV(X, Y)}{\sigma_X \sigma_Y} = \frac{E[(X - \mu_X)(Y - \mu_Y)]}{\sigma_X \sigma_Y} +$$ + +## Spearman Correlation Coefficient + +The Spearman correlation is commonly used in non-linear correlations. It is a measure of the monotonicity of the relationship between two variables X and Y. It has a value between +1 and −1, where 1 is total positive monotonicity, 0 is no monotonicity, and −1 is total negative monotonicity. + +$$ + \rho = \frac{COV(rank(X), rank(Y))}{\sigma_{rank(X)} \sigma_{rank(Y)}} = \frac{E[(rank(X) - \mu_{rank(X)})(rank(Y) - \mu_{rank(Y)})]}{\sigma_{rank(X)} \sigma_{rank(Y)}} +$$ + +## Kendall Correlation Coefficient + +The Kendall correlation is commonly used in non-linear correlations. It is a measure of the ordinal association between two measured quantities. It has a value between +1 and −1, where 1 is total positive association, 0 is no association, and −1 is total negative association. + +This is the most robust correlation coefficient. But is also the most computationally expensive. + +## P-value + +P-value is the probability of obtaining test results at least as extreme as the results actually observed during the test, assuming that the null hypothesis is correct. The smaller the p-value, the stronger the evidence against the null hypothesis. + +- p < 0.001: strong evidence that the null hypothesis is false +- p < 0.05: moderate evidence that the null hypothesis is false +- p < 0.1: weak evidence that the null hypothesis is false +- p > 0.1: no evidence that the null hypothesis is false + +### References + + + + diff --git a/my-brain/data-science/image.png b/my-brain/data-science/image.png new file mode 100644 index 0000000000000000000000000000000000000000..c2a62f4b87e1c771ca5cfeb680f74eeed968c4d0 GIT binary patch literal 129010 zcmZsCRa6`e)Z{>r!NTA!0|a+>88kp}m*5th5FCQLy9alN;O-8=-Q5WioSkp?{QI)| zHmAF%N6ziKb*t)zDJe*!Arm44006YlG7>5P09*|K0J98)g&raBRj&j9$N`@v#MIni z&V&%%)YWGaHayW`VBu!4Jg_7s3PMXlX^k(ds=OC}R-Rt0XlO1rUYu0nB*nMK|Ml1+e8OtjR%nDtBwFj2*-lW;Ku>VjfFltaCL1c6V+E`aBG$@dY zS>AR;{w|+MjPt@}PRJqu{irnY@pRILBO+&pql;JLr#^sJ+UC+SXIEd^{6S6uIRu%9 zynbM15?Iu+z7nmp9fOH=Iw2p1?%LIAmFBD?*39DE3%JDCHfrMcX`#|KqtSS0@N40z 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