Contents
How to do log log regression with sales index?
I have the following log-log regression equation (natural log was used): ln(Sales Index) = B0 + B1 * ln(advertising spend) + B2 * (January) …. + e where advertising spend is a continuous variable (is never zero) and January is a dummy variable. The Sales Index is never zero either.
When to use a logarithmic variable in regression analysis?
The simplest case is when we have logarithmic scales as both dependent and independent. Then we can interpret the coefficient as the expected change in percent in the dependent variable when the independent variable is increased by one percent.
How to use an index in a multiple regression?
You go right ahead and include that index (in levels) in the model you wish to estimate. The interpretation is the same always, when the x increase by 1 y increase by β. You can log the index, provided it is never 0. Then you have a standard level-log model, with the semi elastic interpretation.
How to interpret log transformations in a linear model?
OK, you ran a regression/fit a linear model and some of your variables are log-transformed. Only the dependent/response variable is log-transformed. Exponentiate the coefficient, subtract one from this number, and multiply by 100. This gives the percent increase (or decrease) in the response for every one-unit increase in the independent variable.
How to use a dummy variable in regression?
The interpretation of a dummy variable in a model with a logged dependent variable is in a sense asymmetric: it depends on whether you’re turning January “on” (from 0 to 1) or turning January “off.” Let $Y$be your sales index and $X$your January dummy.
Since this is just an ordinary least squares regression, we can easily interpret a regression coefficient, say β 1, as the expected change in log of y with respect to a one-unit increase in x 1 holding all other variables at any fixed value, assuming that x 1 enters the model only as a main effect.
How are dummy variables interpreted in semilogarithmic equations?
Discussion on the interpretation of the coefficients of dummy variables when the dependent variable is log-transformed is given in: Halvorsen, R. and Palmquist, P., “The Interpretation of Dummy Variables in Semilogarithmic Equations”, American Economic Review, Vol. 70, 1980, pp. 474-475.