Influencing variable and target variable

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In statistics , the target variable is the characteristic that is influenced and thus the object of investigation. It is therefore also called a dependent variable or declared variable . The influencing variables are called influencing variables or explanatory variables . The relationship between the influencing and target variables cannot be determined exactly because it is overlaid by an additive, unobservable disturbance variable .

Model approach

In simple linear regression

{\ displaystyle y_ {i} = \ beta _ {0} + \ beta _ {1} x_ {i} + \ varepsilon _ {i}}

designated

{\ displaystyle y_ {i}}

the target variable (cf. stimulus-response model ), also called target variable or endogenous variable .

${\ displaystyle x_ {i}}$ the explanatory variable, also called the independent variable, predictor variable or exogenous variable .

${\ displaystyle \ varepsilon _ {i}}$ the disturbance . In relation to a measurement series, contains all stochastic error components of the measurement compared to the ideal deterministic model. ${\ displaystyle \ varepsilon _ {i}}$

${\ displaystyle x}$	${\ displaystyle y}$
Influencing factor	Target size
independent variable	dependent variable
explanatory variable	declared variable
Predictor variable	predicted variable
Regressor	Recourse
exogenous variable	endogenous variable

Typically, the target variable chosen is that variable that exhibits natural variability . A simple example is the representation of the body weight in kg (here:) depending on the body size in cm (here:) . You can see that the target size and the influencing size are not interchangeable, since the body size remains unchanged from a certain age. ${\ displaystyle y}$ ${\ displaystyle x}$ ${\ displaystyle y}$ ${\ displaystyle x}$

Measurement

Although their significance is disputed, however, is often noted that a unit variance methods (Engl. Common-method variance ) can occur when the dependent and the independent variable is measured using the same method, for example. In the same questionnaire.

Exogenous and endogenous variables

In statistical and econometric models , an exogenous variable is a variable that is determined outside the model and represents the input of a model. In contrast, endogenous variables are determined within the model and thus represent the output of a model.

Regression

Regression describes regressors as explanatory variables that exert a determinable influence on the variable to be explained ( regressand , explained variable). The regressand only represents the dependent variable. A regressor is considered significant if its influence on the regressand is recognized as not random. In addition to significance , other properties such as independence and completeness can be formulated.

Special features of the regression analysis

Regressors are part of regression analysis and should not simply be viewed as independent variables. The regression analysis is a structure-checking procedure and assumes independence and also makes other assumptions regarding the regressors. A regressor is therefore not an independent variable, because independence is only assumed. Whether a regressor actually exhibits this property can only be determined in the course of the analysis. It is therefore not clear a priori (in advance) whether a regressor actually represents an explanatory variable and whether it has a significant effect on the regressand.

Examples

Example 1: In general, one can assume that independently determined advertising expenditure or independently determined quality of products both have a positive effect on their sales. With the help of statistical analyzes it can now be checked whether an increase in advertising or quality increases sales significantly and how strong the (relative) effect of the two regressors advertising expenditure and quality is on sales.

Example 2: There is an unmarked button on a radio. One possible hypothesis is that it can be used to regulate the volume. Prediction: turning the button in one direction should turn the radio down, turning it in the other direction should make it louder. This hypothesis is tested in the experiment .

Example 3: You want to know whether the color has an influence on the sales of a car. Then color is the independent variable and paragraph is the dependent variable. On the other hand, if you want to know whether the paragraph influences the color, then the paragraph is the independent variable and the color is the dependent variable.

Individual evidence

^ HA Richardson, MJ Simmering, MC Sturman: A tale of three perspectives: Examining post hoc statistical techniques for detection and correction of common method variance. In: Cornell University School of Hotel Administration. 2009, accessed January 26, 2020 .

[1] HA Richardson, MJ Simmering, MC Sturman: A tale of three perspectives: Examining post hoc statistical techniques for detection and correction of common method variance. In: Cornell University School of Hotel Administration. 2009, accessed January 26, 2020 .