dependent variable

Examples of dependent variable in the following topics:

• Slope and Intercept

  • The general purpose is to explain how one variable, the dependent variable, is systematically related to the values of one or more independent variables.
  • An independent variable is so called because we imagine its value varying freely across its range, while the dependent variable is dependent upon the values taken by the independent.
  • Here, by convention, $x$ and $y$ are the variables of interest in our data, with $y$ the unknown or dependent variable and $x$ the known or independent variable.
  • Linear regression is an approach to modeling the relationship between a scalar dependent variable $y$ and one or more explanatory (independent) variables denoted $X$.
  • An equation where y is the dependent variable, x is the independent variable, m is the slope, and b is the intercept.

• Using the Model for Estimation and Prediction

  • Standard multiple regression involves several independent variables predicting the dependent variable.
  • Standard multiple regression is the same idea as simple linear regression, except now we have several independent variables predicting the dependent variable.
  • We would use standard multiple regression in which gender and weight would be the independent variables and height would be the dependent variable.
  • This could happen because the covariance that the first independent variable shares with the dependent variable could overlap with the covariance that is shared between the second independent variable and the dependent variable.
  • Multiple regression is the same idea as single regression, except we deal with more than one independent variables predicting the dependent variable.

• Predictions and Probabilistic Models

  • It includes many techniques for modeling and analyzing several variables when the focus is on the relationship between a dependent variable and one or more independent variables.
  • More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
  • Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed.
  • Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables.
  • Regression analysis is also used to understand which among the independent variables is related to the dependent variable, and to explore the forms of these relationships.

• Qualitative Variable Models

  • Dummy, or qualitative variables, often act as independent variables in regression and affect the results of the dependent variables.
  • In regression analysis, the dependent variables may be influenced not only by quantitative variables (income, output, prices, etc.), but also by qualitative variables (gender, religion, geographic region, etc.).
  • A dummy independent variable (also called a dummy explanatory variable), which for some observation has a value of 0 will cause that variable's coefficient to have no role in influencing the dependent variable, while when the dummy takes on a value 1 its coefficient acts to alter the intercept.
  • The intercept (the value of the dependent variable if all other explanatory variables hypothetically took on the value zero) would be the constant term for males but would be the constant term plus the coefficient of the gender dummy in the case of females.
  • One type of ANOVA model, applicable when dealing with qualitative variables, is a regression model in which the dependent variable is quantitative in nature but all the explanatory variables are dummies (qualitative in nature).

• Regression Analysis for Forecast Improvement

  • In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.
  • Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are fixed.
  • Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables.
  • Regression analysis is also used to understand which among the independent variables is related to the dependent variable, and to explore the forms of these relationships.
  • Regression analysis shows the relationship between a dependent variable and one or more independent variables.

• Variables

  • In this example, relief from depression is called a dependent variable.
  • In general, the independent variable is manipulated by the experimenter and its effects on the dependent variable are measured.
  • An important distinction between variables is between qualitative variables and quantitative variables.
  • Qualitative variables are sometimes referred to as categorical variables.
  • In contrast, the dependent variable "memory test" is a quantitative variable since memory performance was measured on a quantitative scale (number correct).

• Controlling for a Variable

  • Controlling for a variable is a method to reduce the effect of extraneous variations that may also affect the value of the dependent variable.
  • In causal models, a distinction is made between "independent variables" and "dependent variables," the latter being expected to vary in value in response to changes in the former.
  • In other words, an independent variable is presumed to potentially affect a dependent one.
  • In a scientific experiment measuring the effect of one or more independent variables on a dependent variable, controlling for a variable is a method of reducing the confounding effect of variations in a third variable that may also affect the value of the dependent variable.
  • For example, in an experiment to determine the effect of nutrition (the independent variable) on organism growth (the dependent variable), the age of the organism (the third variable) needs to be controlled for, since the effect may also depend on the age of an individual organism.

• Multiple Regression Models

  • One of the measurement variables is the dependent ($Y$) variable.
  • The rest of the variables are the independent ($X$) variables.
  • You've gone to a number of beaches that already have the beetles and measured the density of tiger beetles (the dependent variable) and several biotic and abiotic factors, such as wave exposure, sand particle size, beach steepness, density of amphipods and other prey organisms, etc.
  • A second use of multiple regression is to try to understand the functional relationships between the dependent and independent variables, to try to see what might be causing the variation in the dependent variable.
  • Describe how multiple regression can be used to predict an unknown $Y$ value based on a corresponding set of $X$ values or understand functional relationships between the dependent and independent variables.

• Explanatory and response variables

  • Sometimes the explanatory variable is called the independent variable and the response variable is called the dependent variable.
  • However, this becomes confusing since a pair of variables might be independent or dependent, so we avoid this language.
  • If there are many variables, it may be possible to consider a number of them as explanatory variables.
  • The explanatory variable might affect response variable.
  • In some cases, there is no explanatory or response variable.

• Correlation and Causation

  • A positive correlation means that as one variable increases (e.g., ice cream consumption) the other variable also increases (e.g., crime).
  • Causation refers to a relationship between two (or more) variables where one variable causes the other.
  • change in the independent variable must precede change in the dependent variable in time
  • it must be shown that a different (third) variable is not causing the change in the two variables of interest (a.k.a., spurious correlation)
  • This diagram illustrates the difference between correlation and causation, as ice cream consumption is correlated with crime, but both are dependent on temperature.