Regression Line

 The regression line is the type of line that is used to describe the behaviour of datasets. It also gives the best trend for the given data. It is useful in forecasting procedures.  Its main purpose is to define the interrelation of the dependent variable with one or many independent.

The equation obtained by the regression line acts as an analyst which can forecast the future behaviour of the dependent variables by inputting different values for the independent ones.

Regression Line Formula

y = a + bx + c

Multiple Regression Line Formula

 y= a + b₁x₁ +b₂x₂ + b₃x₃ +…+ b_tx_t + c

It is used in the financial sector and business. It is used by analysts in the finance sector to predict the stock prices, commodity prices and to perform valuations for many different securities. It is also used for predicting sales, inventories, and many other variables.

Properties

• Its coefficients values remain the same because shifting of origin takes place because of change in scale. 
•  If there is two lines of regression both of these lines intersect at a particular point.  According to the property, the intersection of both the lines of regression i.e. y on x and y is [x’, y’]. This is the solution for both of the equations of variables x and y.
• The correlation coefficient between the two variables x and y is the geometric mean of both the coefficients. And the sign used by both the coefficients will be the same. According to the property regression coefficients are b_yx= (b) and b_xy= (b’) then the correlation coefficient is R=+((-sqrt) b_yx + b_xy) therefore, in some cases, both the coefficients give a negative value and  R is also negative.