Statistics Basics & Regression analysis

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It includes a wide range of techniques for describing and analyzing data, including descriptive statistics (such as mean, median, and mode) and inferential statistics (such as estimation and hypothesis testing).

Some key concepts in statistics include:

Probability: the branch of mathematics that deals with the study of chance and random phenomena.

Descriptive statistics: the branch of statistics that deals with the description and summarization of data. This includes measures of central tendency (such as mean, median, and mode) and measures of dispersion (such as range, variance, and standard deviation).

Inferential statistics: the branch of statistics that deals with drawing conclusions about a population based on a sample of data. This includes estimation (such as point estimation and interval estimation) and hypothesis testing (such as t-tests and ANOVA).

Random variables: a variable whose possible values are numerical outcomes of a random phenomenon.

Probability distributions: the set of probability of all possible outcomes for a random variable. For example, the normal distribution, binomial distribution, poisson distribution etc

Sampling: the process of selecting a subset of individuals from a population to study.

Experimentation: the process of conducting controlled studies to test hypotheses and draw conclusions about cause-and-effect relationships.

Regression analysis: a set of statistical processes for estimating the relationships among variables.

Regression analysis is a set of statistical methods used to estimate the relationships between variables. It is used to model the relationship between a dependent variable (also known as the response or outcome variable) and one or more independent variables (also known as predictor or explanatory variables). The goal of regression analysis is to find the line of best fit that describes the relationship between the variables, and to make predictions about the value of the dependent variable based on the values of the independent variables.

There are several different types of regression analysis, including:

Simple linear regression: used to model the relationship between a single independent variable and a dependent variable. The line of best fit is a straight line.

Multiple linear regression: used to model the relationship between multiple independent variables and a dependent variable. The line of best fit is a plane in multi-dimensional space.

Non-linear regression: used to model non-linear relationships between variables.

Logistic regression: used to model the relationship between a binary dependent variable and one or more independent variables.

Poisson regression: used to model count data, such as the number of occurrences of an event.

In regression analysis, the line of best fit is represented by a mathematical equation called the regression equation. The coefficients in the equation represent the estimated effect of each independent variable on the dependent variable, and are used to make predictions about the value of the dependent variable based on the values of the independent variables.

Regression analysis also includes methods for assessing the quality of the fit of the model, such as R-squared and p-values, and for assessing the uncertainty in the estimates of the coefficients in the regression equation, such as confidence intervals.

Regression analysis is a powerful tool for understanding and predicting the relationships between variables, and is widely used in fields such as economics, finance, marketing, and the social sciences.