
Review of Short Phrases and Links 
This Review contains major "Residuals" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Residuals are the deviations of the observed values on the dependent variable from the predicted values, given the current model.
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 Residuals are used to investigate the lack of fit of a model to a given subject.
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 Residuals are the deviation of the data points from the fitted curve.
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 Residuals are useful for examining the assumptions of your general linear model.
 Residuals are the vertical distances of each point from the regression line.
 Mapping the residuals from the regression analysis demonstrated a pattern of greater residuals above the rectosigmoid junction (data not shown).
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 In regression analysis, the distinction between errors and residuals is subtle and important, and leads to the concept of studentized residuals.
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 In a regression analysis, the residuals are the differences between the observed values and the values that are predicted by the regression model.
 Residuals can be tested for homoscedasticity using the BreuschPagan test, which regresses square residuals to independent variables.
 The assumption of homoscedasticity is that the residuals are approximately equal for all predicted DV scores.
 The key properties for the residuals are lack of correlation with the independent variables, independence, and homoscedasticity.
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 Cook statistics depends on the residuals a s well.
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 A general method for resampling residuals is proposed.
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 Regress on to obtain the initial estimators and compute residuals.Under the null hypothesis that, are consistent estimators of.
 The martingale residuals are skewed because of the single event setting of the Cox model.
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 EDF= errordf
specifies the error degrees of freedom if the input observations are residuals from a regression analysis.
 The smaller the sum of squared residuals, the better the fit of the ANOVA model.
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 Run the Spatial Autocorrelation tool on the residuals to ensure they do not exhibit statistically significant spatial clustering.
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 Unlike the errors, however, residuals are correlated, with nonconstant variance.
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 Therefore, this residual is parallel to the raw residual in OLS regression, where the goal is to minimize the sum of squared residuals.
 Run an OLS regression of y on X and construct a series of residuals e[t].
 When the GARCH model is estimated, the normality test is obtained using the standardized residuals.
 Its formula uses the standardized residuals but the modified Cook statistics uses the deletion residuals.
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 Residuals against explanatory variables not in the model.
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 The upper right one is a plot of residuals versus the ﬁtted values (y’s).
 STATA begins regression analysis with computation of case weights from scaled residuals.
 The PDLREG procedure can also test for autocorrelated residuals and perform autocorrelated error correction using the autoregressive error model.
 The R= and RM= options specify output variables for the corresponding residuals, computed as the actual value minus the predicted value.
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 The AUTOREG procedure can produce two kinds of predicted values for the response series and corresponding residuals and confidence limits.
 Durbin J: Tests for serial correlation in regression analysis based on the periodogram of leastsquares residuals.
 To compare maximum likelihood and leastsquares residuals we can analyse the behaviour of their gradients.
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 The HarveyCollier test performs a ttest (with parameter degrees of freedom) on the recursive residuals.
 The test statistic used is based on recursive residuals.
 The slope of the partial residuals will be the same as for the regression, but a lowess smoothing line may be drawn to highlight curvature of the data.
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 Additive models: regression curve is a sum of partial response functions; partial residuals and the backfitting trick generalize.
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 When using GEE, the mean and median correlations estimated using Pearson residuals were negative.
 By default, this uses a (double) maximum statistic of Pearson residuals.
 Pearson residuals and its standardized version is one type of residual.
 There seems to be more than just the plots of the Pearson residuals and deviance residuals below.
 We'll get both the standardized Pearson residuals and deviance residuals and plot them against the predicted probabilities.
 Traditionally it is estimated from the deviance residuals, reported by ASReml as Variance heterogeneity.
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 There were large residuals of 0.235, 0.119, 0.138, and 0.144 between the BWSQB and other variables (BDEPQ, BAI, & BDI).
 The GM (DRGP) is a GMestimator with the main aim as downweighting high leverage points with large residuals.
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 If the data are obtained in a time (or space) sequence, a residuals vs.
 Studentized residuals are useful in testing for outliers.
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 Studentized residuals (11) are the fitted residual rescaled to have the same variance as the corresponding theoretical distribution.
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 In this case, the sum of the squared residuals is 0.09+0.16+0.64+2.25+0.04 = 3.18.
 The response in a regression is identically equal to the fit of the regression plus the residuals (the regression line plus distance to the line).
 This method finds a line (plane or hyperplane) that minimizes a robust estimate of the scale (from which the method gets the S in its name) of the residuals.
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 Technically, it is the line that "minimizes the squared residuals".
 It is used in calculation of the modified Cook's distance instead of standardized residuals.
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 Then, in step 536, the routine estimates the amounts of fuel, residuals and air in cylinder at IVC via equations 5.265.30.
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 Finally, in step 538, the routine updates intake manifold states (mass of gaseous fuel, residuals, air, and liquid fuel puddle) via equations 5.315.34.
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 PCSEs are calculated using the OLS residuals from equation (3).
 Residuals from a regression of the 1990 Census poverty rates for 1989 for all people under age 5 years on the 1989 values of these three variables.
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 The variable s y.x quantifies the average size of the residuals, expressed in the same units as Y. Some books and programs refer to this value as s e.
 Moreover, it ensured normality of residuals and enforced prediction values to be within the physical range of a variable.
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 Figure 3 displays the residuals of the LBNN estimates against the LBNN fitted values of ŷ.
 The autocorrelation check of residuals is shown in Figure 3.13.
 The following SAS code uses the GPLOT procedure to plot the residuals obtained from the OLS estimation, as shown in Figure 3.
 Different levels of variability in the residuals for different levels of the explanatory variables suggests possible heteroscedasticity.
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 Thus to compare residuals at different inputs, one needs to adjust the residuals by the expected variability of residuals, which is called studentizing.
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 When the plot of residuals appears to deviate substantially from normal, more formal tests for heteroscedasticity should be performed.
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 F tests for autoregressive conditional heteroscedastic (ARCH) disturbances: These test statistics are computed from the residuals of the ARCH(1) model.
 F tests for AR disturbance: These test statistics are computed from the residuals of the univariate AR(1), AR(2), AR(3), and AR(4) models.
 Tests of causality in variance in multiple time series have been proposed recently, based on residuals of estimated univariate models.
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 The paper considers smallsample aspects of this procedure when the periodogram is calculated from the residuals from leastsquares regression.
 The underlying goal is to find an appropriate formula so that the residuals are as small as possible and exhibit no pattern.
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 Existing scale estimators are based on the residuals from an estimator of the regression itself.
 Consequently this average of squares of residuals is maximumlikelihood estimate of σ 2, and its square root is the maximumlikelihood estimate of σ.
 It is shown that the definitions of the resulting bootstrap replications fi differ only with respect to the regarded residuals or the used matrix of weights.
 This set of conditions is an important one and it has a number of implications for the properties of the fitted residuals and the modelled values.
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 These fixed values are included by necessity: they set the scale of measurement for the latent factors and residuals.
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 Below is Gauss code with a procedure that calculates the BoxPierce statistic for a set of residuals.
 Commutativity of this monoid implies that the two residuals coincide as a → b.
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 If the relationship is linear and the variability constant, then the residuals should be evenly scattered around 0 along the range of fitted values (Fig.
 If the standard statistical model is to apply, then the residuals should be scattered about the line y = 0 with “normally” distributed values.
 Heteroscedasticity is indicated when the residuals are not evenly scattered around the line.
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 Easily save results (coefficients, coefficient covariance matrices, residuals, gradients, etc.) to EViews objects for further analysis.
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 Regression
 Encyclopedia of Keywords > Thought > Value > Values
 Test Statistics
 Residual
 Mathematics > Statistics > Normal Distribution > Normality
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