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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

A regional gallery records visitor numbers each quarter. Set t=1 for the first observation and increase t by 1 for each subsequent observation

Observed values
PeriodGallery visitors (visitors)
2018 Q3455
2018 Q4439
2019 Q1423
2019 Q2407
2019 Q3391
2019 Q4375
2020 Q1359

The fitted model for the measured values is:

\[\hat{y}=471-16t\]

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 Gallery visitors in visitors on the vertical axis. The plotted points are (t=1, 455), (t=2, 439), (t=3, 423), (t=4, 407), (t=5, 391), (t=6, 375), (t=7, 359). A fitted straight trend segment runs from (1, 455) to (7, 359).2018 Q32019 Q12019 Q32020 Q1300350400450500fitted trendTime period tGallery visitors(visitors)
(a)1 mark

Map the target period 2020 Q2 to its consecutive time index t

(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

Interpret the fitted slope for Gallery visitors

(d)1 mark

Use the fitted trend to estimate the gallery visitors for 2020 Q2. Give your answer to 1 decimal place

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

Judge the use of the fitted line for the target period