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Partial Residual Plot
In applied statistics, a partial residual plot is a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model. Background When performing a linear regression with a single independent variable, a scatter plot of the response variable against the independent variable provides a good indication of the nature of the relationship. If there is more than one independent variable, things become more complicated. Although it can still be useful to generate scatter plots of the response variable against each of the independent variables, this does not take into account the effect of the other independent variables in the model. Definition Partial residual plots are formed as : \text + \hat_iX_i \text X_i, where : Residuals = residuals from the full model, : \hat_i = regression coefficient from the ''i''-th independent variable in the full model, : ''X''i = the '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Statistics
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphical Technique
Statistical graphics, also known as statistical graphical techniques, are graphics used in the field of statistics for data visualization. Overview Whereas statistics and data analysis procedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial form. They include plots such as scatter plots, histograms, probability plots, spaghetti plots, residual plots, box plots, block plots and biplots. Exploratory data analysis (EDA) relies heavily on such techniques. They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection. In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the underlying message that is present in the data to others. Graphical statistical methods h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent Variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable). Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Response Variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable). Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" ( Herman Adèr quoting Kenneth Bollen). All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. Introduction Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that the assumption allows us to calculate the probability of any event. As an example, consider a pair of ordinary six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called '' simple linear regression''; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regressio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scatter Plot
A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded (color/shape/size), one additional variable can be displayed. The data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis. Overview A scatter plot can be used either when one continuous variable is under the control of the experimenter and the other depends on it or when both continuous variables are independent. If a parameter exists that is systematically incremented and/or decremented by the other, it is called the ''control parameter'' or independent variable and is customarily plotted along the horizontal axis. The measured or dependent variable is cu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Errors And Residuals In Statistics
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its " true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the '' estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full Model
{{disambiguation ...
Full may refer to: * People with the surname Full, including: ** Mr. Full (given name unknown), acting Governor of German Cameroon, 1913 to 1914 * A property in the mathematical field of topology; see Full set * A property of functors in the mathematical field of category theory; see Full and faithful functors * Satiety, the absence of hunger * A standard bed size, see Bed * Fulling, also known as tucking or walking ("waulking" in Scotland), term for a step in woollen clothmaking (verb: ''to full'') * Full-Reuenthal, a municipality in the district of Zurzach in the canton of Aargau in Switzerland See also *"Fullest", a song by the rapper Cupcakke *Ful (other) Ful or FUL may refer to: * Fula language * Fula people * Ful medames, a fava bean dish of Sudan and Egypt * Fullerton Municipal Airport, California, United States; IATA code FUL * Fullerton Transportation Center, California; Amtrak code FUL * Ful (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Regression Plot
In applied statistics, a partial regression plot attempts to show the effect of adding another variable to a model that already has one or more independent variables. Partial regression plots are also referred to as added variable plots, adjusted variable plots, and individual coefficient plots. When performing a linear regression with a single independent variable, a scatter plot of the response variable against the independent variable provides a good indication of the nature of the relationship. If there is more than one independent variable, things become more complicated. Although it can still be useful to generate scatter plots of the response variable against each of the independent variables, this does not take into account the effect of the other independent variables in the model. Calculation Partial regression plots are formed by: #Computing the residuals of regressing the response variable against the independent variables but omitting ''X''i #Computing the residuals f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Leverage Plot
In regression analysis, partial leverage (PL) is a measure of the contribution of the individual independent variables to the total leverage of each observation. That is, if ''h''''i'' is the ''i''th element of the diagonal of the hat matrix, PL is a measure of how ''h''''i'' changes as a variable is added to the regression model. It is computed as: : \left(\mathrm_j\right)_i = \frac where :''j'' = index of independent variable :''i'' = index of observation :''X''''j''· 'j''/sub> = residuals from regressing ''X''''j'' against the remaining independent variables Note that the partial leverage is the leverage of the ''i''th point in the partial regression plot for the ''j''th variable. Data points with large partial leverage for an independent variable can exert undue influence on the selection of that variable in automatic regression model building procedures. See also * Leverage * Partial residual plot * Partial regression plot * Variance inflation factor for a multi- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance Inflation Factor
In statistics, the variance inflation factor (VIF) is the ratio (quotient) of the variance of estimating some parameter in a model that includes multiple other terms (parameters) by the variance of a model constructed using only one term. It quantifies the severity of multicollinearity in an ordinary least squares regression analysis. It provides an index that measures how much the variance (the square of the estimate's standard deviation) of an estimated regression coefficient is increased because of collinearity. Cuthbert Daniel claims to have invented the concept behind the variance inflation factor, but did not come up with the name. Definition Consider the following linear model with ''k'' independent variables: : ''Y'' = ''β''0 + ''β''1 ''X''1 + ''β''2 ''X'' 2 + ... + ''β''''k'' ''X''''k'' + ''ε''. The standard error of the estimate of ''β''''j'' is the square root of the ''j'' + 1 diagonal element of ''s''2(''X''′''X'')−1, where ''s'' is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
