Log-Linear Trend Models

A log-linear trend model is used to regress a seemingly exponential series on time. The estimated coefficients are $$ b_0 = 1.791$$ and $$b_1 = 0.094 $$. The estimated value in period 24 is about:

Incorrect. This can be calculated by using the coefficients as estimated with a linear trend model rather than with a log-linear trend model.

Correct! The model estimates $$ ln \, y_t = b_0 + b_1t + \epsilon_t $$, and would then estimate a period 24 value of $$ ln \, \hat{y}_t = 1.791 + 0.094(24) $$, leading to $$ \hat{y} = e^{1.791 + 0.094(24)} = 57.226 $$.

Incorrect. Consider that the model estimates $$ ln \, y_t = b_0 + b_1t + \epsilon_t $$, using the estimated parameters given to solve for _y_ in period 24.

4\.

57\.

192\.