Let’s have an example of regression .A new plant to manufacture widgets was set up, the plant’s personnel manager advertises the employment opportunity in the plant and the very next morning it has 2000 people waiting for applying to the 100 available jobs. It will be important to select the best of 100 people who will cut above the rest employees because the training of these people will involve both time and money and firing the employee is going to be difficult as well as bad for community relations. In order to overcome this situation and to help make correct decision an analysis is adopted by the Personnel manager, this analysis is the Regression analysis. A Regression analysis is used to predict the purposes and to understand relationship between two variables x and y. It is used when two or more variables are systematically connected by a linear relationship. A Multivariate Regression Analysis is a technique that estimates a single regression model with more than one outcome variable.
In a Regression equation, y is the dependent variable and x is a independent variable, the Regression Formula can be given as y’= a +bx; where y’ is the estimated y which is on the y-axis from the point on the regression line for the predictor x value, x is an arbitrary chosen value of the predictor variable for which the corresponding value of the criterion variable is desired, a is the intercept point of the regression line and the y-axis and b is the slope of the regression line. a and b are calculated as follows,
a = [sigma(y)][sigma(x2)] – [sigma(x)][sigma(x)(y)]divided by {n [sigma(x2)]- [sigma(x)]2} and
b= n[sigma(xy)] – [sigma(x)][sigma(y)] divided by {n [sigma(x2)]- [sigma(x)]2}
Regression Analysis Example or Regression Example: Regression analysis is an analysis to assess the values of the given parameters for a particular function that cause the function to the best utilize a set of observed datas that are given. For example, if we take into account the value of an automobile, it decreases constantly with a certain amount each year after the purchase, and each for mile it has driven, the related linear function would predicts its value as a function of the two independent variables like ‘age’ and ‘miles’: value = price + dep age x age + dep miles x miles; where value is the dependent variable which is the value of the car, age is the age of the car and the miles is the number of miles that the car has covered. The regression analysis done determines the best of values of the three parameters, price, the estimated value when the age is zero, dep-age, which is the depreciation that takes place each year, dep-miles is the depreciation for each mile driven. The values of dep-age and dep-miles will be -ve as the car would be losing value as the car age and the miles covered increase.
