It is discarded in calculating the coefficients 26 An illustrative example

It is discarded in calculating the coefficients 26 an

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It is discarded in calculating the coefficients.26
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An illustrative example using Venn diagramsYXBlueZRedGreenOrangeBecause the contribution in red is not discernible whether it comes from Z or X it is not used and only unique variation in blue and greenare used leading tounbiased estimates.In this example are the SLR models of Y on Z and Y on X producing unbiased estimates?No, both produce biased estimates. Here including the variables in the MLR leads to unbiased estimates at the cost of higher variances which is almost always the case.27
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An illustrative example using Venn diagramsYXBlue00000ZGreenHow about now?Are the SLR models producing unbiased estimates?Yes. There is no correlation in the independent variables now. These variables are said to be orthogonal.28
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An illustrative example using Venn diagramsYXBlue00000ZGreenWhat is this illustrating?There is now a great deal correlation in the independent variables.RedThis is foreshadowing the MLR assumptions but you can easily see that little unique variation is left for the estimation of the coefficients on X and Z.And using similar logic as before the variances on these estimators will be quite high.29
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An illustrative example using Venn diagramsYXYellowBlueZRedGreenOrangeConceptually speaking what do you think R2looks like here?Here the ratio of the (Blue + Red + Green) to the ratio (Blue + Red + Green + Yellow) is R2.30
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An illustrative example using Venn diagramsYXYellowBlueZRedGreenOrangeFinally, what is Yellow representing?31
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An illustrative example using Venn diagramsYXYellowBlueZRedGreenOrangeWhich implies what if we remove an independent variable?That’s right the error variance is larger.32
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