Explanation:

From the regression equation, $\hat{\beta}_0 = 5.105$ and $\hat{\beta}_1 = 0.044$ . 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}

The calculation shows that the trend value estimate for the 90th week is 8,647.28 million.

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 90th week?

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NNikitesh

Last updated: February 2, 2026 at 10:22

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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 90th week?