Statistical Models and how businesses use Regression Analysis.

Statistical models used for various types of Analytics.

Type of Analytics	Purpose	Examples of Methodologies
Descriptive	To identify possible trends in large data sets or databases. The purpose is to get a rough picture of what generally the data looks like and what criteria might have potential for identifying trends or future business behavior.	Descriptive statistics, including measures of central tendency (mean, median, mode), measures of dispersion (standard deviation), charts, graphs, sorting methods, frequency distributions, probability distributions, and sampling methods.
Predictive	To build predictive models designed to identify and predict future trends.	Statistical methods like multiple regression and ANOVA. Information system methods like data mining and sorting. Operations research methods like forecasting models.
Prescriptive	To allocate resources optimally to take advantage of predicted trends or future opportunities.	Operations research methodologies like linear programming and decision theory.

How businesses use Regression analysis

Regression analysis is a statistical tool used for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another — the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate.

Regression analysis is used to estimate the strength and the direction of the relationship between two linearly related variables: X and Y. X is the "independent" variable and Y is the "dependent" variable.

Covariance Implications:

Covariance calculation shows the direction of the relationship as well as its relative strength. If one variable increases and the other variable tends to also increase, the covariance would be positive. If one variable goes up and the other tends to go down, then the covariance would be negative. It basically evaluates the relationship between the variables.

Correlation coefficient Implications:

Covariance is standardized in order to better interpret and use it in forecasting, and the result is the correlation calculation. The correlation calculation simply takes the covariance and divides it by the product of the standard deviation of the two variables. This will bound the correlation between a value of -1 and +1. A correlation of +1 can be interpreted to suggest that both variables move perfectly positively with each other, and a -1 implies they are perfectly negatively correlated.

The two basic types of regression analysis are:

·         Simple regression analysis: Used to estimate the relationship between a dependent variable and a single independent variable; for example, the relationship between crop yields and rainfall.

A simple linear regression model is given as y = bx + a

The "y" is the value we are trying to forecast, the "b" is the slope of the regression, the "x" is the value of our independent value, and the "a" represents the y-intercept. The regression equation simply describes the relationship between the dependent variable (y) and the independent variable (x).

·         Multiple regression analysis: Used to estimate the relationship between a dependent variable and two or more independent variables; for example, the relationship between the salaries of employees and their experience and education.

Regression analysis is based on several strong assumptions about the variables that are being estimated. Several key tests are used to ensure that the results are valid, including hypothesis tests. These tests are used to ensure that the regression results are not simply due to random chance but indicate an actual relationship between two or more variables.

An estimated regression equation may be used for a wide variety of business applications, such as:

·         Measuring the impact on a corporation's profits of an increase in profits

·         Understanding how sensitive a corporation's sales are to changes in advertising expenditures

·         Seeing how a stock price is affected by changes in interest rates