The result of a quadratic model fit to time-series data was $\ddot{\mathbf{p}}_{t}= 8.5 - 0.25 t + 2.5 t ^ { 2 }$ , where t = 1 for 1994. The forecast value for 2001 is 129.25.

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To forecast for 2001, we calculate $t = 2001 - 1994 + 1 = 8$. Substituting $t = 8$ into the model $\ddot{\mathbf{p}}_{t}= 8.5 - 0.25t + 2.5t^2$, we get $\ddot{\mathbf{p}}_{8}= 8.5 - 0.25(8) + 2.5(8)^2 = 8.5 - 2 + 160 = 166.5$, not 129.25.

The Result of a Quadratic Model Fit to Time-Series Data p¨t=8.5−0.25t+2.5t2\ddot{\mathbf{p}}_{t}= 8.5 - 0.25 t + 2.5 t ^ { 2 }p¨​t​=8.5−0.25t+2.5t2

The Result of a Quadratic Model Fit to Time-Series Data $\ddot{\mathbf{p}}_{t}= 8.5 - 0.25 t + 2.5 t ^ { 2 }$