Q.Using the trend equation obtained for the firm's profit data in the earlier example ($Y_c = 18 + 4.6X$, origin 2020, $X$ in years), estimate the firm's expected profit for 2023 and 2024.

Because the least squares method gives an actual equation, it can be extended beyond the given years simply by substituting the appropriate future value of $X$. …

The trend equation fitted earlier, with origin at 2020 and $X$ measured in years, is:

Since 2020 corresponds to $X=0$, the year 2023 is 3 years after the origin ($X=3$) and 2024 is 4 years after the origin ($X=4$).

For 2023 ($X=3$):

For 2024 ($X=4$):

Independent check. The trend rises by exactly $b=4.6$ for every one-year increase in $X$; from the last known trend value at 2022 ($Y_c=27.2$, at $X=2$), adding $4.6$ once gives $27.2+4.6=31.8$ (2023), and adding it again gives $31.8+4.6=36.4$ (2024) — matching the direct substitution above. …

Forgetting that a forecast from a fitted trend line is conditional on past conditions continuing — presenting it as a certainty rather than …