note06 - 1 Chapter 6 Multiple Regression Analysis further...

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1 Chapter 6. Multiple Regression Analysis: further Issues Effects of Data Scaling Change in the scale of the dependent variable all coefficients are affected by the same scale standard deviation of the error term is also affected by the same scale no change in the hypothesis test, but the confidence interval changes Change in the scale of explanatory variable affect only the coefficient of the variables involved Note: it is desirable to scale the explanatory variables of a similar magnitudes. This increases the numerical accuracy of estimation procedure. Functional Forms A choice of functional relationship gives different interpretation of estimated parameters. For example, In this equation, measures the percentage change in y when changes by 1%. This interpretation is based on the approximation of logarithmic function by the Taylor expansion around 1. Applying this to , the change in can be approximated by Thus, if the dependent variable increases by 0.1, then it is approximately equivalent to a 10% increase in y . Let . What is the percentage change in y ? The approximation described above says 100c%. What is the exact percentage change in y ?
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2 Taking exponential on both sides, we get Therefore, the exact percentage change is . The difference between this true percentage change and the approximated percentage change can be large if c is large. Therefore, when c is large, it is better to compute the true percentage change. The magnitude of the difference is shown in the figure below where each percentage change is shown against the values of c .
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