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1 of 8 0-day streak

Fit a time trend and forecast

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
Non-seasonal supplied model; within or one period from the observed intervalNon-seasonal supplied model; cautious the observed intervalNOWMix of allRecommended
Question 1 of 8

Calculator allowed

The table records pool attendance each quarter from 2021 Q3. Set t=1 for the first observation and increase t by 1 for each subsequent observation

Observed values
PeriodPool attendance (visits)
2021 Q3521
2021 Q4543
2022 Q1565
2022 Q2587
2022 Q3609
2022 Q4631

The fitted model for the measured values is:

\[\hat{y}=499+22t\]

Use the exact coefficients shown in the model. Round only final numerical answers to 1 decimal place

Cartesian time-series graph with time period t on the horizontal axis and Pool attendance in visits on the vertical axis. The plotted points are (t=1, 521), (t=2, 543), (t=3, 565), (t=4, 587), (t=5, 609), (t=6, 631). A fitted straight trend segment runs from (1, 521) to (6, 631).2021 Q32022 Q12022 Q22022 Q4500550600650fitted trendTime period tPool attendance(visits)
(a)1 mark

Use the calendar labels to identify the target period number

(b)2 marks

Read the intercept a and slope b from the supplied fitted model. Give both values to 1 decimal place

(c)1 mark

Choose the statement that gives the meaning of b in this model

(d)1 mark

Use the fitted trend to estimate the pool attendance for 2023 Q1. Give your answer to 1 decimal place

Format: 1 d.p.
(e)1 mark

Is the target an interpolation or an extrapolation, and what limitation applies?