The same variable has a dozen names depending on who measures it
A statistician calls it a regressor, an economist a control variable, a doctor a risk factor, and a machine-learning engineer a feature. They all mean roughly the same thing: the input you change or track, while watching something else respond. The quantity doing the responding carries just as many aliases.
In mathematics a function takes an input and returns an output. The symbol for an arbitrary input is the independent variable, usually x, and the symbol for the output is the dependent variable, usually y, as in y = f(x). There can be several of each: in z = f(x, y), both x and y feed a single result z, while functions with several outputs are called vector-valued.
Experiments use the same logic. The researcher manipulates the independent variable and watches for changes in the dependent one. Studying fertiliser, you vary the amount applied and measure the plant's height or mass, while keeping the plant type, pot size and sunlight fixed; those fixed factors are controlled variables. Heating beetroot samples to different temperatures and measuring how much pigment leaks out follows the same pattern, as does adding sugar to coffee and noting the taste.
Real studies are messier. Extraneous variables, such as age, class or intelligence in a study of how college affects lifetime earnings, can influence the result without being the focus, and leaving an influential one out of a regression can distort the conclusions. They come in three kinds: traits of the people studied, traits of the experimenters, and features of the setting such as lighting, temperature or time of day. Whatever the independent variables fail to explain is lumped into an error or residual term.
Some authors prefer explanatory and response variables, because inputs are not always truly independent of each other. In a 1987 analysis of sea level trends by Woodworth, time served as the main input and yearly mean sea level as the outcome; adding annual mean air pressure as a covariate gave better estimates of the trend.
Source: Dependent and independent variables
