The line which expresses the trend of two observed values is called a regression line. For example if the sample data is given then the value of y corresponding to the given value of x can be estimated by the method of least squares. Now because the value of y is estimated from given value of x therefore the resulting line is called regression line of y on x which means that y is dependent on x. on the other hand if the value of x is estimated from given value of y then the resulting line is called regression line of x on y which means that x is dependent on y.
The general equation of y on x is Y= a+bx whereas the equation of x on y is X= c+dy. Here b and d are the slope of regression lines of y on x and x on y respectively. a and b measure the rates of change of one variable in terms of other and are also known as the regression coefficients. The procedure for calculating the regression lines of y on x and x on y are given as:
Problem: The following table shows the chart of price and demand for an item at different periods of time.
Forecast demand for the price of $ 25
Predict price for the demand of 35 kilograms
Thus if the price of item is $25 then the demand will be 34.03Kg whereas in case of 35Kg demand the price will be $23.61.