By William Greene

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For example, when a 0/1 dummy variable is included to measure promotions, this transformation cannot be applied. In that case, A continuous dependent variable 33 one simply considers the 0/1 dummy variable. The elasticity of such a dummy variable then equals expðk Þ À 1. Often one is interested in quantifying the eﬀects of explanatory variables on the variable to be explained. 6). For example, it may be that sales are correlated with price and advertising, but that they are not correlated with display or feature promotion.

In practice, the values of and 2 are unknown, but they could be estimated from the data. In many cases, however, one may expect that marketing instruments such as prices, advertising and promotions do have an impact on sales. 2 Scatter diagram of yt against xt where the value of the mean is now made dependent on the value of the explanatory variable, or, in other words, where the conditional mean of Yt is now a linear function of 0 and 1 xt , with 0 and 1 being unknown parameters. 2, we depict a set of simulated yt and xt , generated by xt ¼ 0:0001t þ "1;t with "1;t $ Nð0; 1Þ yt ¼ À2 þ xt þ "2;t with "2;t $ Nð0; 1Þ; ð3:3Þ where t is 1; 2; .

3, and it is clear that the distribution of the data has become more symmetric. Additionally, the distribution seems to obey an approximate bell-shaped curve. Hence, except for a few large observations, the data may perhaps be summarized by an approximately normal distribution. It is exactly this distribution that underlies the standard Linear Regression model, and in chapter 3 we will take it as a starting point for discussion. 2 of the Appendix at the end of this book. 1 we summarize some characteristics of the dependent variable and explanatory variables concerning this case of weekly sales of Heinz tomato ketchup.