In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values dependent and independent variables pdf independent variables. Functions with multiple outputs are often referred to as vector-valued functions. X appears in an ordered pair with exactly one element of Y.

In this situation, a symbol representing an element of X may be called an independent variable and a symbol representing an element of Y may be called a dependent variable, such as when X is a manifold and the symbol x represents an arbitrary point in the manifold. In an experiment, a variable, manipulated by an experimenter, is called an independent variable. The dependent variable is the event expected to change when the independent variable is manipulated. In mathematical modeling, the dependent variable is studied to see if and how much it varies as the independent variables vary. In simulation, the dependent variable is changed in response to changes in the independent variables. Depending on the context, a dependent variable is sometimes called a “response variable”, “regressand”, “predicted variable”, “measured variable”, “explained variable”, “experimental variable”, “responding variable”, “outcome variable”, “output variable” or “label”. The primary independent variable was time.

A variable may be thought to alter the dependent or independent variables, but may not actually be the focus of the experiment. So that variable will be kept constant or monitored to try to minimize its effect on the experiment. Such variables may be designated as either a “controlled variable”, “control variable”, or “extraneous variable”. Extraneous variables, if included in a Regression analysis as independent variables, may aid a researcher with accurate response parameter estimation, prediction, and goodness of fit, but are not of substantive interest to the hypothesis under examination. Subject variables, which are the characteristics of the individuals being studied that might affect their actions.

These variables include age, gender, health status, mood, background, etc. Blocking variables or experimental variables are characteristics of the persons conducting the experiment which might influence how a person behaves. Gender, the presence of racial discrimination, language, or other factors may qualify as such variables. Situational variables are features of the environment in which the study or research was conducted, which have a bearing on the outcome of the experiment in a negative way. Included are the air temperature, level of activity, lighting, and the time of day. In a study measuring the influence of different quantities of fertilizer on plant growth, the independent variable would be the amount of fertilizer used. The dependent variable would be the growth in height or mass of the plant.

The controlled variables would be the type of plant, the type of fertilizer, the amount of sunlight the plant gets, the size of the pots, etc. In a study of how different doses of a drug affect the severity of symptoms, a researcher could compare the frequency and intensity of symptoms when different doses are administered. In measuring the amount of color removed from beetroot samples at different temperatures, temperature is the independent variable and amount of pigment removed is the dependent variable. Workshop calculus: guided exploration with review. A concrete introduction to real analysis. Introduction to Set Theory, Revised and Expanded.

The Oxford Dictionary of Statistical Terms, OUP. Data Analysis Using Microsoft Excel, New Delhi. This page was last edited on 28 March 2018, at 01:30. In statistics and regression analysis, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator. Moderation analysis in the behavioral sciences involves the use of linear multiple regression analysis or causal modelling.

In this case, the role of x2 as a moderating variable is accomplished by evaluating b3, the parameter estimate for the interaction term. See linear regression for discussion of statistical evaluation of parameter estimates in regression analyses. However, the new interaction term will be correlated with the two main effects terms used to calculate it. This is the problem of multicollinearity in moderated regression. Multicollinearity tends to cause coefficients to be estimated with higher standard errors and hence greater uncertainty. However, mean-centering is unnecessary in any regression analysis, as one uses a correlation matrix and the data are already centered after calculating correlations. Like simple main effect analysis in ANOVA, in post-hoc probing of interactions in regression, we are examining the simple slope of one independent variable at the specific values of the other independent variable.

Below is an example of probing two-way interactions. If both of the independent variables are categorical variables, we can analyze the results of the regression for one independent variable at a specific level of the other independent variable. 1 represents the difference in the dependent variable between males and females when life satisfaction is zero. However, a zero score on the Satisfaction With Life Scale is meaningless as the range of the score is from 7 to 35. When treating categorical variables such as ethnic groups and experimental treatments as independent variables in moderated regression, one needs to code the variables so that each code variable represents a specific setting of the categorical variable.

There are three basic ways of coding: Dummy-variable coding, Effects coding, and Contrast coding. Below is an introduction to these coding systems. Effects coding is used when one does not have a particular comparison or control group and does not have any planned orthogonal contrasts. This coding system is appropriate when the groups represent natural categories. Contrast coding is used when one has a series of orthogonal contrasts or group comparisons that are to be investigated.

In this case, the intercept is the unweighted mean of the individual group means. A and B are two sets of groups in the contrast. If both of the independent variables are continuous, it is helpful for interpretation to either center or standardize the independent variables, X and Z. The principles for two-way interactions apply when we want to explore three-way or higher-level interactions. It is worth noting that the reliability of the higher-order terms depends on the reliability of the lower-order terms. For example, if the reliability for variable A is .

70, and reliability for variable B is . A and B that actually exist. Moderation in management research: What, why, when and how. Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations. This page was last edited on 8 February 2018, at 14:43. In an experiment, the variables used can be classed as either dependent or independent variables.

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