Statistics is a branch of mathematics.
Math is hard and often not intuitive.
Statistics is notoriously unintuitive.
So, to understand statistics you've got to understand the derivation
of its formulas, a process that is neither easy nor obvious.
My goal here is to understand the derivations. I will
often include interactive figures to help with understanding.
chapters
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01_concepts
02_probability
03_binomial_distribution
04_normal_distribution
05_poisson_distribution
06_regression
07_principal_component_analysis
topics
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01 random experiment
01 sample space
01 randon variable
01 prob distribution
01 mean
01 binom PMF norm PDF μ σ2 σ, quartiles
01 variance
01 covariance
01 correlation coeff
01 skewness kurtosis
01 moments
02 p(same or diff birthdays)
03 Bernoulli trial
03 binomial random variable
03 expected values of xi and X
03 binomialDistrEquation
03 binomial distributin mean
03 binomial distr. Var StDev
03 binomial distr. proportion
03 bin. distr. moment generat. function
03 binomial distr. kurtosis
03 normal Vs binomial distr.
03 binomial distr. example
04 normal distr definition
04 normal distr confidence intervals
04 error function
05 Poisson definition derivation
05 Poisson shape
05 Poisson example
05 Poisson Chi Sq
06 using Python in linear regression
06 the coefficients: y-intercept and slope
06 R-squared coeff. determination
06 adjusted R-squared
06 the F statistic
06 the standard errors
06 t-statistics
06 95% CI
06 95% CI limits
06 Log L_AIC_BIC
06 omnibus test
06 Durbin Watson
06 condition number
07 matrices vectors and scalars
07 matrix basic opertations
07 matrices the determinant
07 projections
07 eigenvectors eigenvalues
07 correlation matrices introduction
07 covariance matrices introduction
07 cov corr matrox properties
07 high dimension cov and corr matrices
07 bigger data - a literature example
derivations
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01 var(X)
01 var(cX)
01 var(X+Y)
01 var Σ(Xi)
01 E[X^2]
01 E[mean(X)^2]
01 sample var
01 cov(XY)
01 cov(XX)
01 cov(Xc)
01 cov(aX+bY)
01 cov(X+Z,Y)
01 cov(ΣaY,ΣbY)
01 cov(meanX,meanY)
01 sample cov
01 cov(correlated X,Y)
01 alpha_3
01 alpha_4
04 normal distribution
05 Poisson derivation
06 coefficients calculus
06 coefficients lin. algebra
06 residual std error
06 slope std err
06 slope std err lin alg
06 y-intercept std rr
07 Euclidian norm
07 orthogonal vector product
07 vector onto vector projection
07 vector onto plane projection
07 solving the caracteristic equation
07 symmetric matrix - orthogonal vectors
07 symmetric matrix diagonalizable
07 PDP - PΛQ
07 symmetric matrix real eigenVs
07 PC1 greatest variance
07 power iteration
figures
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01 superimposed bin norm distrib
02 p(same or diff birthdays)
03 binomial stdev vs pq
03 binomial vs normal distr.
04 norm. distr. dart diagram
04 norm. distr. jacobian diagram
04 norm. distr. men and women heights
04 norm. distr. confidence interval for sigma 1
04 norm. distr. 95 % confidence interval
04 norm. distr. two-tail confidence interval
05 Poisson vs binomial
05 Poisson shape
06 using Python in linear regression
06 understanding R-squared TSS/RSS
06 F-statistic test and figure
06 t-statistic test and figure
07 scree plot
07 score plot
07 score calculations
07 loadings plot
interactive
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01 norm_PDF vs binom_PMF
07 vector projection
07 projection onto a plane
07 projection onto any plane
07 projection onto eigenVs
07 power_iteration
python
select
01 superimposed Norm Binom
02 p(same or diff birthdays)
03 binomial stdev vs pq
03 binomial vs normal
04 norm. distr. men and women heights
04 norm. distr. CI of sigma 1
04 norm. distr. 95% CI
04 norm. distr. two-tail CI
05 Poisson vs binomial
06 random lin regress data
06 linear regression
06 understanding R-squared TSS/RSS
06 F-statistic test and figure
06 t-statistic test and figure
07 bigger data calculations and figures
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