1. I have a multiple regression equation where log(salary) = b0 + b1(ceotenure). What is the purpose of putting the dependent variable in logarithmic form? How would you interpret the change in y for a 1 unit increase in ceotenure?

  2. For this multiple regression equation, what are the unit measurements for RMSE?

  3. I have a second multiple regression equation where salary = b0 + ln(sales) + ln(marketvalue). How does the fact that the independent variables are now in natural logarithmic form change the interpretation of a 1 unit increase in x leads to a ____ change in y?

  4. I am asked to add profits to this second equation. It asks why this variable cannot be included in logarithmic form? I have no idea.

  1. You would use this model under the assumption that "salary" increases exponentially with "ceotenure". The log-linear form captures this relationship. For a 1 unit increase in "ceotenure", the salary changes by a multiplicative factor of $e^{b1}$.

  2. I think it should be the same unit as the dependent variable, so probably "log-dollars".

  3. b1*ln(sales) changes to b1*ln(sales+1), and this isn't free from the current level of sales, so an interpretation of the regression coefficient is not easy here.

  4. Profits may be negative. (Loss!)

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  • $\begingroup$ A unit increase in $\ln(\text{sales})$ is the same as multiplying $\text{sales}$ by $e$. More typically we'd examine the effect of say a $1\%$ or $10\%$ increase in sales ($\ln(sales) + \ln(1.01)$ for the log variable, for example) as being more interpretable. $\endgroup$ – Glen_b Jun 28 '14 at 4:47

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