The linear trend model, _t = 660 + 2t starting with t = 1, for seasonally adjusted monthly sales was estimated using monthly data from for five years. Furthermore, the seasonal index for October was found to be 0.92. Which of the following is the forecast for the month of October next year? A) 660 B) 800 C) 736 D) 749

Question

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The linear trend model is given by: _t = 660 + 2t To find the forecast for October next year, we need to find the value of t for October next year and substitute it into the equation. We know that the seasonal index for October is 0.92, which means that the sales for October are typically 92% of the average monthly sales. So, we can use this information to estimate the sales for October next year relative to the average monthly sales: October next year sales = 0.92 x (average monthly sales) To find the value of t for October next year, we need to add 12 to the current year's time value: t = 60 (for December 2018) + 12 = 72 Substitute t = 72 into the linear trend model: _t = 660 + 2t ₇₂ = 660 + 2(72) ₇₂ = 660 + 144 ₇₂ = 804 This gives us the estimated sales for October next year. However, this is not the final answer since this value includes the seasonal effect. To get the final forecast, we need to adjust for the seasonal effect by dividing by the seasonal index: Final forecast = October next year sales / seasonal index Final forecast = 804 / 0.92 = 736 Therefore, the best choice is C, 736.

The Linear Trend Model, t = 660 + 2t

The Linear Trend Model, _t = 660 + 2t