Holiday-park guest nights in a North Island town

Table 1 shows the number of guest nights (in thousands) at holiday parks in a North Island town for each quarter from 2021 Q1 to 2024 Q4 (Q1 = Jan–Mar). An analyst fitted a least-squares linear trend, with time $t = 1$ for 2021 Q1 up to $t = 16$ for 2024 Q4: $$\hat{T} = 53.33 + 0.478t$$The seasonal effects are the mean residuals for each quarter: Q1$+13.1$, Q2$-6.33$, Q3$-10.13$, Q4$+3.36$(thousand guest nights). Figure 1 shows the series with the fitted trend line. Figure 2 shows, for each quarter, the residuals from the trend (data − trend) for each year, together with their mean, which is the seasonal effect. Table 1: Guest nights (thousands) | Quarter |$t$ | Guest nights | |---|---|---| | 2021 Q1 | 1 | 68.1 | | 2021 Q2 | 2 | 47.0 | | 2021 Q3 | 3 | 42.0 | | 2021 Q4 | 4 | 58.3 | | 2022 Q1 | 5 | 66.6 | | 2022 Q2 | 6 | 49.0 | | 2022 Q3 | 7 | 46.3 | | 2022 Q4 | 8 | 57.7 | | 2023 Q1 | 9 | 70.9 | | 2023 Q2 | 10 | 53.0 | | 2023 Q3 | 11 | 48.8 | | 2023 Q4 | 12 | 64.6 | | 2024 Q1 | 13 | 73.5 | | 2024 Q2 | 14 | 54.3 | | 2024 Q3 | 15 | 52.9 | | 2024 Q4 | 16 | 65.3 |