1. Exploratory Data Analysis 1.2. EDA Assumptions 1.2.1. Underlying Assumptions?
Assumptions underlying a measurement process	There are four assumptions which typically underlie all measurement processes, namely, that the data from the process at hand "behave like": random drawings; from a fixed distribution; with that distribution having a fixed location; and with that distribution having a fixed variation.
Univariate or single response variable	The "fixed location" referred to in item 3 above differs for different problem types. The simplest problem type is univariate, that is a single variable. For the univariate problem, the general model response = deterministic component + random component becomes response = constant + error
Assumptions for univariate model	For this case, the "fixed location" is simply the unknown constant. We can thus imagine the process at hand to be operating under constant conditions that produces a single column of data with the properties that the data are uncorrelated with one another; the random component has a fixed distributuion; the deterministic component consists only of a constant; and the random component has fixed variation.
Extrapolation to a function of many variables	The universal power and importance of the univariate model is that it easily extrapolates to the more general case where the deterministic component is not just a constant but is in fact a function of many variables and the engineering objective is to characterize and model the function.
Residuals will behave according to univariate assumptions	The key point is that regardless of how many factors, and regardless of how complicated the function, if the engineer succeeds in choosing a good model, then the differences (residuals) between the raw response data and the predicted values from the fitted model should themselves behave like a univariate process. Further, this univariate process fit will behave like: random drawings; from a fixed distribution; with fixed location (namely, 0 in this case); and with fixed variation.
Validation of model	Thus if the residuals from the fitted model do in fact behave like the ideal, then testing of underlying assumptions becomes a tool for the validation and quality of fit of the chosen model. On the other hand, if the resiudals from the chosen fitted model violate one or more of the above univariate assumptions, then the chosen fitted model is inadequate and an opportunity exists for arriving at an improved model.