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# Ordinary Least Square Uncertainty

 Problems of Regression Model Using Ordinary Least Squares Problem Consequences Check Remedial action Problems due to assumptions of least squares Residuals not normal inferential test procedures based on F test may be invalid Rankit plot: Shapiro W test (and others) Transform y values (Box-Cox transformation). Use of different error models (Generalised linear modelling.) heteroskedasticity Biased estimation of error variance and hence inferential test procedures may be invalid Plot residuals against y . x’s & other variables. Anscombe’s test (and others) Transform y variable y ½ .log(y).y not independent Inferential test procedures may be invalid. Underestimate true sampling variance of regression estimates. Inflated R Residual plots. Some tests (e.g.: Durbin-Watson; space: Moran) Iterated generalised least squares Non linearity of functional relationship Poor fit; meaningless results: non independent residuals Scatterplots of y against x’s. Added variable plots. transforms x’s and/or y variables Problems due to the nature of data Multicollinearity amongst explanatory variable (X Correlation measures. tests based on eigenvalues of (X Transform explanatory variables. Delete variables. Ridge regression Difficulties in performing: efficient analysis sifting out variables Added variable plots for variable selection. Transform x’s and/or y to simplify model. Stepwise regression Outliers and leverage effects May severily distort model fit. Model fit is dependent on a few values. Robust. resistant regression. Data deletion Inacurate data Meaningless results Exploratory data methods may highlights errors Delete or replace inaccurate values Incomplete data Missing at random: could be wasteful of other information if this has to be discarded. Not missing at random: suspect inferences Estimate missing values (missing at random). Reduce data matrix to the cases with full information Categorical “Normal” linear regression model inappropriate Generalised linear model (e.g. logistic regression). Source: nfm

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