What is a Regression Line?

Definition: In statistics, a regression line is a line that best describes the behavior of a set of data. In other words, it’s a line that best fits the trend of a given data.

What Does Regression Line Mean?

What is the definition of regression line? Regression lines are very useful for forecasting procedures. The purpose of the line is to describe the interrelation of a dependent variable (Y variable) with one or many independent variables (X variable). By using the equation obtained from the regression line an analyst can forecast future behaviors of the dependent variable by inputting different values for the independent ones. Regression lines are widely used in the financial sector and in business in general.

Financial analysts employ linear regressions to forecast stock prices, commodity prices and to perform valuations for many different securities. On the other hand, companies employ regressions for the purpose of forecasting sales, inventories and many other variables that are crucial for strategy and planning. The regression line formula is like the following:

(Y = a + bX + u)

The multiple regression formula looks like this:

(Y = a + b1X1 + b2X2 + b3X3 + … + btXt +u.)

  • Y is the dependent variable
  • X is the independent ones
  • a is the interception point
  • b is the slope
  • u is the residual regression

Help Appliances Co. is a company that manufactures professional and home kitchen appliances. The company is currently in the process of forecasting their sales for next year and as part of this procedure the National Sales Manager hired a consulting company to get some advice on how to improve the accuracy of the forecast. The consulting company provided a multiple regression model of 4 independent variables. How would a regression line help the Sales Manager to forecast next year’s sales figure?

As the concept previously displayed shows, a multiple linear regression would generate a regression line represented by a formula like this one: Y = a + b1X1 + b2X2 + b3X3 + b4X4 + u. The Sales Manager will substitute each of the values with the information provided by the consulting company to reach a forecasted sales figure.

Summary Definition

Define Regression Lines: Regression line means a connection between data points in a set.

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