8 Regression Analysis – Linear Models with Non‐random Regressors (Model I of Regression Analysis) and with Random Regressors (Model II of Regression Analysis)
8.1 Introduction
In this chapter we describe relations between two or more magnitudes with statistical methods.
Dependencies between magnitutes can be found in several laws of nature. There is a dependency of the height h of a physical body falling under the influence of gravity (in a vacuum) and the case time t in the form h = αt2, and the relationship provided by this formula is a special function, a so‐called functional relationship. Similar equations can be given for the relationship between pressure and temperature or between brightness and distance from a light source. The relationship is strict, that is, for each value of t, there is a unique h‐value, or in other words, with appropriate accuracy from the same t‐value, there always results a unique h‐value. One could calculate α by the formula above by setting t and measuring h, if there is no measurement error. The h‐values for various t‐values lie on a curve (parabola) when t is plot on the abscissa and h on the ordinate of a coordinate system. In this example, you could give h as well and measure the time. In functional relationships, therefore, it doesn't matter which variable is given and which is measured, if no other aspects (accuracy, effort in the measurement), which have nothing to do with the context itself, lead to the preference of one of these variables. ...