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Logs In Regression - Statistics Department

Statistics 621 Robert StineFall, 2001 1 Logs Transformation in a Regression EquationLogs as the PredictorThe interpretation of the slope and intercept in a Regression change when thepredictor (X) is put on a log scale. In this case, the intercept is the expected valueof the response when the predictor is 1, and the slope measures the expectedchange in the response when the predictor increases by a fixed properties of the Regression equation are most clear in the context of anexample, such as the display example from the casebook. In that example, theestimated least squares Regression equation isSales = 84 + 139 log(Feet)To interpret the intercept 84 in this equation, we need to remove the term involvingthe slope. If the number of feet is 1, then the estimated equation becomesSales = 84 + 139 log(1) = 84 + 139 (0) = 84So, as promised, the intercept is the expected level of sales (here, $84) when thenumber of feet used in the display is set to s a little harder to figure out the meaning of the slope.

Statistics 621 Robert Stine Fall, 2001 5 as long as the changes are “small” relative to past values. Thus we have shown that on average, sales increase 3.4% per period. Logs as the Predictor and the Response In this case, the coefficient is known as an elasticity. Elasticities are described ...

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