Outsourcing Analytical Services - Regression Analysis

Regression Analysis is a commonly used Statistical tool to determine the relationship between variables. It more correctly examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables).

For example, the value of a car keeps diminishing with the number of miles and age. In this case the Value (dependent/response variable) is related to the Number of miles and Age of the car (Independent variables/explanatory variables).

A very common example to explain Regression analysis is the relation of various factors to Income. There may be a number of factors that influence Income such as age, education, experience, type of employment/occupation etc.

Some Examples Include:

- The Family expenditure (dependent variable) influenced by Income, number of children etc (independent variable).

- The Influence of various mediums of advertising such as print, media, Internet (Independent) on Sales (dependent variable).

- Sales Forecasting can be done using time series data to include in influencers such as Seasonal fluctuations etc.

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Some commonly used Terminology:

A regression equation outlines the relationship between two (or more) variables algebraically. It indicates the nature of the relationship between two (or more) variables and the extent to which you can predict some variables by knowing others or based on its association with others.

The regression equation is represented on a scatter plot by a regression line.

A regression line is a line drawn through the points on a scatter plot to summarize the relationship between the variables. It indicates a negative or inverse relationship between the variables when it slopes from top left to bottom right and a positive or direct relationship is when it slopes from bottom right to top left.

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Least squares are a method used for fitting a specified model to observed data.

Multiple linear regression is aimed at finding a linear relationship between a response variable and many possible explanatory variables.

Nonlinear regression aims to detail the relationship between a response variable and one or more explanatory variables in a non-linear fashion.

The multiple regression correlation coefficient, (R²) is a measure of the proportion of variability explained by, or due to the linear relationship in a sample of paired data. It is a number between zero and one and a value close to zero suggests a poor model.

A very high value of can arise even though the relationship between the two variables is non-linear. The fit of a model should never simply be judged from the R² value.

A' regression model is sometimes developed in stages. A list of several explanatory variables is available and is repeatedly searched for variables which should be included in the model. The best explanatory variable is used first, and then the second best and the process continues. This procedure is known as Stepwise regression.

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