Dependent and independent variables

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In mathematical modeling, statistical modeling, and experimental science, the value of dependent variable depends on the value of the independent variable . The dependent variable represents the output or the result of which variations are being studied. The independent variable, also known in the statistical context as regresor , represents the input or cause, that is, the potential reason for the variation or, in the experimental setting, the variable controlled by the experiment. Models and experiments test or determine the effect that independent variables have on the dependent variable. Sometimes, independent variables can be included for other reasons, such as for potential confounding effects, without the desire to test their effects directly.

Video Dependent and independent variables

Matematika

In math, the function is the rule to take input (in the simplest case, a number or a series of numbers) and provide output (which can also be numeric). Symbols that are abbreviations of random input are called independent variables , while symbols representing random outputs are called dependent variables . The most common symbols for the input are x , and the most common symbol for the output is y ; the function itself is usually written ${\ displaystyle y = f (x)}$ .

Dimungkinkan untuk memiliki beberapa variabel independen dan/atau beberapa variabel dependen. Misalnya, dalam kalkulus multivariabel, seseorang sering menemukan fungsi bentuk ${\ displaystyle z = f (x, y)}  ÂÂ$ , di mana z adalah variabel dependen dan x dan y mandiri variabel. Fungsi dengan beberapa output sering disebut sebagai fungsi bernilai vektor.

In set theory, the function between a set of X and a set of Y is part of Cartesian product ${\ displaystyle X \ times Y}$ so that every element X appears in pairs that are sorted with exactly one Y element. In this situation, the symbol representing the X element can be called an independent variable and the symbol representing the Y element can be called the dependent variable, as when X is the manifold and the symbol x represents any point in the manifold. However, many advanced textbooks do not distinguish between dependent and independent variables.

Statistics

In experiments, variables, manipulated by an experiment, are called independent variables (X). The dependent variable (Y) is the expected event change when the independent variables are manipulated.

In the data mining tool (for multivariate statistics and machine learning), the dependent variable is assigned role as target variable (or in some tools as attribute labels ), whereas independent variables can be assigned as regular variables . A known value for the target variable is provided for the training data set and test data set, but must be predicted for other data. Target variables are used in supervised learning algorithms but not in unattended learning.

Modeling

Dalam pemodelan matematika, variabel dependen dipelajari untuk melihat apakah dan berapa banyak bervariasi karena variabel independen bervariasi. Dalam model linear stochastic sederhana ${\ displaystyle y_ {i} = a bx_ {i} e_ {i}}  ÂÂ$ istilah ${\ displaystyle y_ {i}}  ÂÂ$ adalah nilai i ^th dari variabel dependen dan ${\ displaystyle x_ {i}}  ÂÂ$ adalah nilai i ^th dari variabel independen. Istilah ${\ displaystyle e_ {i}}  ÂÂ$ dikenal sebagai "kesalahan" dan berisi variabilitas variabel dependen yang tidak dijelaskan oleh variabel independen.

Dengan beberapa variabel independen, modelnya adalah ${\ displaystyle y_ {i} = a bx_ {1, i} bx_ {2, i} ... bx_ {n, i} e_ {i }}  ÂÂ$ , di mana n adalah jumlah variabel independen.

Simulasi

In the simulation, the dependent variable is changed in response to changes in the independent variable.

Maps Dependent and independent variables

Synonym stats

Depending on the context, independent variables are sometimes called "predictor variables", regression , covariates , "controlled variables", "variable manipulations", "explanatory variables", exposure variables (see reliability theory), "risk factors" (see medical statistics), "features" (in machine learning and pattern recognition) or "input variables." In econometrics, the term "control variable" is usually used instead of "covariate".

Depending on the context, the dependent variable is sometimes called "response variable", "regressand", "criterion", "predictor variable", "measured variable", "described variable", "experimental variable", "response variable", " result variable "," output variable "or" label ".

The "Explanatory Variables" are preferred by some authors over "independent variables" when the amounts treated as independent variables may not be independently statistically or manipulated independently by the researcher. If the independent variable is referred to as "explanatory variable" then the term "response variable" is preferred by some authors for the dependent variable.

The "explained variable" is preferred by some authors over "dependent variables" when the amount treated as "dependent variable" may not be statistically dependent. If the dependent variable is referred to as the "described variable" then the term "predictor variable" is preferred by some authors for independent variables.

Variables can also be referred to by the form: continuous, binary/dichotomous, categorical nominal, and ordinal categorical, among others.

An example is provided by an analysis of trends at sea level by Woodworth (1987). Here the dependent variable (and the most interesting variable) is the average annual mean sea level at a particular location in which a series of annual values ​​is available. The main independent variable is time. The use is made of a covariate composed of annual mean annual atmospheric pressure values ​​at sea level. The results showed that inclusion of covariates enabled an increase in the estimated trend against time to be obtained, compared with analyzes that eliminated covariates.

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Other variables

A variable may be considered to change a dependent or independent variable, but may not be the focus of the experiment. So that variable will remain constant or monitored to try to minimize its effect on the experiment. Such variables can be defined as "control variables", "control variables", or "foreign variables".

External variables, if included in the regression analysis as independent variables, may assist the researcher with accurate response estimation, prediction, and goodness of fit, but have no substantive importance to the hypothesis tested. For example, in a study examining the effect of post-secondary education on lifetime income, some foreign variables may be gender, ethnicity, social class, genetics, intelligence, age, and so on. The variable is foreign only when it can be assumed (or displayed) to influence the dependent variable. If included in the regression, it can improve the suitability of the model. If it is excluded from the regression and if it has a non-zero covarianant with one or more of the desired independent variables, its negligence will be the regression result biased for the effect of an attractive independent variable. This effect is called a confusing or omitted variable bias; In this situation, design changes and/or controls for statistical control variables are required.

External variables are often grouped into three types:

1. Subject variables, which are characteristics of learned individuals that may affect their actions. These variables include age, gender, health status, mood, background, etc.
2. Blocking an experimental variable or variable is a characteristic of a person doing an experiment that may affect a person's behavior. Gender, presence of racial discrimination, language, or other factors may be qualified as such variables.
3. Situational variables are environmental features where research or research is conducted, which has an effect on the experimental results in a negative way. Includes air temperature, activity level, lighting, and time of day.

In modeling, the variability not covered by the independent variable is specified by ${\ displaystyle e_ {I}}$ and known as "rest", "side effects", "errors", "unspecified shares", "residual variable" ".

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Example

• The effect of fertilizer on plant growth

In a study that measures the effect of different amounts of fertilizers on plant growth, its independent variables are the amount of fertilizer used. Dependent variables are high growth or plant mass. Controlled variables are plant types, fertilizer types, amount of sunlight obtained by plant, size of pot, etc.

• The effect of a drug dose on the severity of the symptoms

In a study of how different doses of drugs affect the severity of the symptoms, a researcher can compare the frequency and intensity of the symptoms when different doses are given. Here the free variable is the dose and the dependent variable is the frequency/intensity of the symptom.

• The effect of temperature on pigmentation

In measuring the amount of color removed from the beetroot samples at different temperatures, the temperature is an independent variable and the number of deleted pigments is a dependent variable.

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Also see

• Abscissa
• Ordinate
• Blocking (statistics)

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Reference

Source of the article : Wikipedia