One of the problems often dealt in Statistics is minimization of the objective function. And contrary to the linear models, there is no analytical solution for models that are nonlinear on the parameters such as logistic regression, neural networks, and nonlinear regression models (like Michaelis-Menten model). In this situation, we ... [Read more...]

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Consider the linear regression model, $$ y_i=f_i(\boldsymbol{x}|\boldsymbol{\beta})+\varepsilon_i, $$ where $y_i$ is the response or the dependent variable at the $i$th case, $i=1,\cdots, N$ and the predictor or the independent variable is the $\boldsymbol{x}$ term defined in the mean function $... [Read more...]

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Ever wonder what's the mathematics behind face recognition on most gadgets like digital camera and smartphones? Well for most part it has something to do with statistics. One statistical tool that is capable of doing such feature is the Principal Component Analysis (PCA). In this post, however, we will not ... [Read more...]

Enough with the theory we recently published, let's take a break and have fun on the application of Statistics used in Data Mining and Machine Learning, the k-Means Clustering.k-means clustering is a method of vector quantization, originally from signa... [Read more...]

Interval estimation of the population mean can be computed from functions of the following R packages:stats - contains the t.test;TeachingDemos - contains the z.test; and,BSDA - contains the zsum.test and tsum.test.The t.test of the stats package is a ... [Read more...]

Skewness and kurtosis in R are available in the moments package (to install a package, click here), and these are:Skewness - skewness; and,Kurtosis - kurtosis.Example 1. Mirra is interested on the elapse time (in minutes) she spends on riding a tricycl... [Read more...]