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Regression residuals

Regression residuals. LS Residuals. Standardized residuals. s I is an estimate of the standard deviation of. s (I) is an estimate computed from the regression that excludes the ith observation. t residuals. Diagnostics for model assumptions. Linearity Residual plots: look for curvature

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Regression residuals

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  1. Regression residuals • LS Residuals • Standardized residuals sIis an estimate of the standard deviation of s(I)is an estimate computed from the regression that excludes the ith observation • t residuals

  2. Diagnostics for model assumptions • Linearity • Residual plots: look for curvature • Transformations ofx’s or/and y: log, Square, reciprocal. . . • Constancy of the error variance s2 • Residual plots : look for change in the spread • Tests • Transformations: log, Square root, . . .

  3. Diagnostics for model assumptions • Normality of the error term e • Normal probability plot of the residuals • Tests of normality for the residuals • Transformations of y: log, Square root, . . . • Uncorrelated errors Corr(ei ,ej ) = 0 • Residual plots : look for patterns • DW and other tests • Transformations: Differencing, percent change, . .

  4. Influential and Outlying Observations • Measures of influence of an observation • Cook Distance Di • Leverage hii

  5. Collinearity Problem • High linear relationship among the x’s • Some symptoms • F-ratio significant but t-ratios not significant • Unusually large LS coefficient bj • Meaningless sign for a LS coefficient bj

  6. Collinearity Diagnostics • Pairwise correlation Corr(xj , xk) • Rj2 for regression of xj on other x’s • Variance Inflation Factor

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