independent variable

Examples of independent variable in the following topics:

• Using the Model for Estimation and Prediction

  • Standard multiple regression involves several independent variables predicting the dependent variable.
  • In addition to telling us the predictive value of the overall model, standard multiple regression tells us how well each independent variable predicts the dependent variable, controlling for each of the other independent variables.
  • As mentioned, the significance levels given for each independent variable indicate whether that particular independent variable is a significant predictor of the dependent variable, over and above the other independent variables.
  • Because of this, an independent variable that is a significant predictor of a dependent variable in simple linear regression may not be significant in multiple regression (i.e., when other independent variables are added into the equation).
  • 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.

• Variables

  • In this case, the variable is "type of antidepressant. " When a variable is manipulated by an experimenter, it is called an independent variable.
  • The experiment seeks to determine the effect of the independent variable on relief from depression.
  • In general, the independent variable is manipulated by the experimenter and its effects on the dependent variable are measured.
  • If an experiment were comparing five types of diets, then the independent variable (type of diet) would have 5 levels.
  • In general, the number of levels of an independent variable is the number of experimental conditions.

• 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.

• 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.
  • In all cases, the estimation target is a function of the independent variables, called the regression function.

• Regression Analysis for Forecast Improvement

  • The independent variables are measured with no error.
  • 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.
  • In all cases, the estimation target is a function of the independent variables called the regression function.
  • Regression analysis shows the relationship between a dependent variable and one or more independent variables.

• Controlling for a 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 experiments, independent variables include factors that can be altered or chosen by the researcher independent of other factors.
  • There are also quasi-independent variables, which are used by researchers to group things without affecting the variable itself.
  • 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.

• Multiple Regression Models

  • One of the measurement variables is the dependent ($Y$) variable.
  • The rest of the variables are the independent ($X$) variables.
  • Then, if you went to a beach that didn't have tiger beetles and measured all the independent variables (wave exposure, sand particle size, etc.), you could use the multiple regression equation to predict the density of tiger beetles that could live there if you introduced them.
  • 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.

• Qualitative Variable Models

  • Dummy, or qualitative variables, often act as independent variables in regression and affect the results of the dependent variables.
  • Dummy variables are "proxy" variables, or numeric stand-ins for qualitative facts in a regression model.
  • 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.
  • 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).

• 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).
  • A negative correlation is just the opposite; as one variable increases (e.g., socioeconomic status), the other variable decreases (e.g., infant mortality rates).
  • 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)