Multiple regression analysis (MRA) is a useful method for generating mathematical models where there are several (more than two) variables involved. Some applications are listed at the end of this topic.
In order to appreciate the topic more easily the reader is recommended to read the topic of Regression and correlation, to be found elsewhere on this website.
In that topic one can see that a simple regression model or formula has the following basic form: y = a + bx where a is a constant, fixed value, b is a coefficient of the variable x and y is the result to this equation.
This is a simple model describing a situation where there is only one independent variable, b (the dependent variable being y, because the value of y depends on the value taken by x). The example given in the other topic was:
Time to load a van = 3.4 + (0.3 x number of parcels) minutes.
This is simple regression and is in the form of a straight line in this instance. However, the regression line often is in the form of a curve of best fit such as a parabola y = bx2 or hyperbola or other function. Where two independent variables are involved we have multiple regression and correlation and the model will not be a line but a plane. If more than two independent variables then the model is built up of hyperplanes which cannot be visualized, but can be represented by a mathematical model, which takes the general form for n independent variables as:
Y = a + b1x1 + b2x2 + b3x3 + b4x4 + ... + bnxn
This could refine the model. In addition to the number of parcels which mostly are different we could add (a) total weight carried in kg. and (b) total volume in cubic metres.
Y = 2.6 + 4.1(number of parcels) + 1.8(weight) + 0.9(volume)
In addition to the coefficients (b1, b2, etc) for the model the computer package will also provide a full validation analysis for the results including a value known as the R-squared measure which is an evaluation of the reliability of the model as predictor of the Y values. It is the multiple correlation factor squared. Other statistical tests are also performed by the program to assess the reliability of each of the coefficients and the constant in the formula.
Other tests include measuring the intercorrelations between any of the variables.
These tests must be considered when evaluating the usefulness and validity of the model in predicting the basic time for work carried out under different circumstances.