Multiple Regression



Multiple Regression

Introduction

This paper discusses the multiple regression method used for predicting the values of Y; multiple regressions are a general and flexible statistical method for analyzing associations between two or more independent variables and a single dependent variable.

As a general statistical technique, multiple regressions can be employed to predict values of a particular variable based on knowledge of its association with known values of other variables, and it can be used to test scientific hypotheses about whether and to what extent certain independent variables explain variation in a dependent variable of interest. As a flexible statistical method, multiple regressions can be used to test associations among continuous as well as categorical variables, and it can be used to test associations between individual independent variables and a dependent variable, as well as interactions among multiple independent variables and a dependent variable. In this entry, different approaches to the use of multiple regression are presented, along with explanations of the more commonly used statistics in multiple regression, methods of conduction multiple regression analysis, and the assumptions of multiple regression.

Regression analysis uses a mathematical equation to describe this kind of relationship. In linear regression the equation describes the straight line which, on the average, provides the closest "fit" to all the points at once. There is only one such line and it is known as the least-squares regression line. It gets its name from the fact that if we measure the vertical distance (called a residual) between the line and each point on the graph, square each distance, and adds them up, the total will be smaller for this line than for any other. Hence, it is the line that best "fits" the data.

The general form of the equation is Y=a+bX, where Y is the predicted value of the dependent variable and X is the value of the independent variable. The caret (^) over the Y indicates that it is a predicted rather than an actual value. The regression constant (also known as the Y-intercept), which is represented by a in the equation, tells us the value of Y when X has a value of zero. It is also the point where the line crosses the vertical (Y) axis. The regression coefficient (or slope), which is represented by b in the equation, tells us how much the value of Y changes for each change in X.

Method

In this paper we have discussed one common application of multiple regressions for predicting values of dependent variable i.e. Y, based on knowledge of its association with certain independent variables (i.e. Predictors X1, X2, X3 and X4). In this context, the independent variables are commonly referred to as predictor variables and the dependent variable is characterized as the criterion variable. In applied settings, it is often desirable for one to be able to predict a score on a criterion variable by using information that is available in certain predictor variables. The data has been collected from the forecast_data.xls, after placing the data in the Excel sheet, ...