The tractor maker actually sold 150 thousand…

The tractor maker actually sold 150 thousand in 2024.

Question 63

MediumOriginal question

A tractor maker fits the trend $y = 120 + 6x$ to its yearly sales, where $y$ is sales in thousands and $x$ is years counted from 2020 ( $x = 0$ in 2020).

The tractor maker actually sold 150 thousand in 2024. What does the gap between this and the trend show?

The trend is wrong and must be refittedCorrect answerYour answerSales were 6 thousand below trendCorrect answerYour answerThe long-run trend has risen to 150Correct answerYour answerSales were 6 thousand above trend, from short-term movementsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

2024 is $x = 4$ : the trend gives $120 + 24 = 144$ .
$150 - 144 = 6$ above trend: the part the trend leaves to seasonal, cyclical and irregular movements.

Worth noting

A single year off the line does not make the trend wrong; real values scatter around it.

Concept: Actual values against the trend
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsA straight-line trend by least squares

Practise this chapter →

Ten questions from Time Series & Trend, at your own pace.

Practise this chapter →

Ten questions from Time Series & Trend, at your own pace.

The tractor maker actually sold 150 thousand in 2024.

Question 63

Explanation