In Statistics, Linear regression refers to a model that can show relationship between two variables and how one can impact the other. In essence, it involves showing how the variation in the “dependent variable” can be captured by change in the “independent variables”.
In Business, this dependent variable can also be called the predictor or the factor of interest for eg., sales of a product, pricing, performance, risk etc. Independent variables are also called explanatory variables as they can explain the factors that influence the dependent variable along with the degree of the impact which can be calculated using “parameter estimates” or “coefficients”. These coefficients are tested for statistical significance by building confidence intervals around them so that the model that we are building is statistically robust and based on objective data. The elasticity based on the coefficient can tell us the extent to which a certain factor explains the dependent. Further, a negative coefficient can be interpreted to have a negative or an inverse relation with the dependent variable and positive coefficient can be said to have a positive influence. The key factor in any statistical models is the right understanding of the domain and its business application.
Linear Regression is a very powerful statistical technique and can be used to generate insights on consumer behaviour, understanding business and factors influencing profitability. Linear regressions can be used in business to evaluate trends and make estimates or forecasts. For example, if a company’s sales have increased steadily every month for the past few years, by conducting a linear analysis on the sales data with monthly sales, the company could forecast sales in future months.
Linear regression can also be used to analyze the marketing effectiveness, pricing and promotions on sales of a product. For instance, if company XYZ, wants to know if the funds that they have invested in marketing a particular brand has given them substantial return on investment, they can use linear regression. The beauty of linear regression is that it enables us to capture the isolated impacts of each of the marketing campaigns along with controlling the factors that could influence the sales. In real life scenarios there are multiple advertising campaigns that run during the same time period. Supposing two campaigns are run on TV and Radio in parallel, a linear regression can capture the isolated as well as the combined impact of running this ads together.
Linear Regression can be also used to assess risk in financial services or insurance domain. For example, a car insurance company might conduct a linear regression to come up with a suggested premium table using predicted claims to Insured Declared Value ratio. The risk can be assessed based on the attributes of the car, driver information or demographics. The results of such an analysis might guide important business decisions.
In the credit card industry, a financial company maybe interested in minimizing the risk portfolio and wants to understand the top five factors that cause a customer to default. Based on the results the company could implement specific EMI options so as to minimize default among risky customers.
While Linear regression has limited applicability in business situations because it can work only when the dependent variable is of continuous nature, it still is a very well known technique in the situations it can be used. It assumes a linear relation between the independent and dependent variables. It must be noted that sometimes transformations can also be applied to non linear relationships to make them applicable in a linear regression model.