An investment analyst wants to fit the weekly sales (in millions) of his company by using the sales data from Jan 2018 to Feb 2019. The regression equation is defined as: $ \ln Y_t = 5.105 + 0.044t, \quad t = 1, 2, ..., 100 $ What is the trend value estimate of the sales in the $90^{th}$ week? | Financial Risk Manager Part 1 Quiz

An investment analyst wants to fit the weekly sales (in millions) of his company by using the sales data from Jan 2018 to Feb 2019. The regression equation is defined as:

\ln Y_t = 5.105 + 0.044t, \quad t = 1, 2, ..., 100

What is the trend value estimate of the sales in the $90^{th}$ week?_

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Explanation:

From the regression equation, $\hat{\beta}_0 = 5.105$ and $\hat{\beta}_1 = 0.044$ . We know that, under log-linear trend models, the predicted trend value is given by:

\ln Y_t = \hat{\beta}_0 + \hat{\beta}_1 t \\ \Rightarrow Y_t = e^{\hat{\beta}_0 + \hat{\beta}_1 t} \\ \therefore Y_{90} = e^{5.105 + 0.044 \times 90} \\ = e^{5.105 + 3.96} \\ = e^{9.065} \\ = 8,647.28 \text{ Million} $$_

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