Statistics part-2: Regression Analysis

 

This article serves to explain all of necessary fundamentals for Regression Analysis reference for posting formulae: 

https://www.calculatorsoup.com/calculators/statistics/

Average (or) Arithmetic Mean of the data:

A dataset constitutes several data points and can have several properties that are described by several parameters. Every dataset has a central location around which all of its data points cluster or scatter around. This central location is called the "Average" or "Arithmetic Mean" of that dataset. "Arithmetic Mean" or simply "Mean" ( for this discussion context, we can shortly call it as Mean) is one of measures of central tendency. As all data points center around this statistical term "Mean", it is considered to be the single point general description of all data points in the given data set. "Mean" has to be computed as it doesn't physically exist. Sometimes, one of data points can have exact value as that of "Mean" of that entire dataset. 

Consider a hurricane that has storm winds swirling around its center. Without its eye, a hurricane doesn't exist. We can think of the eye of a hurricane as its mean around which its winds swirl. In other words, its winds have the tendency to center around or cluster around its eye. The eye is a calm zone with no chaos. Just as the "Mean" that doesn't exist in the given dataset unless explicitly computed, a hurricane's eye has no visible presence if you are plotting hurricane's destructive power throughout its body on a destruction scale. Despite lacking the visible destructive trait of a hurricane, its eye acts as its "Mean" to describe the hurricane size, magnitude and other properties. Average (or) mean is calculated by dividing summation of all data points in a data set by its size n. 

Mean=x¯¯¯=∑ni=1xin

Variance