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Time Series & Trend · Question 59 of 68

Question 59

MediumOriginal question

A straight-line trend y=a+bxy = a + bx is fitted by least squares to the output 30, 34, 37, 41 and 48 for 2020 to 2024, with xx in years from 2022. What is aa?

Options for question 59

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. With x=−2,−1,0,1,2x = -2, -1, 0, 1, 2, ∑x=0\sum x = 0, so a=∑yna = \frac{\sum y}{n}.

  2. a=1905=38a = \frac{190}{5} = 38.

Worth noting

37 is the 2022 value itself; aa is the mean of all five.

Concept
The intercept when the years are centred
Typical time
90 s
Your time
—
The rule this testsA straight-line trend by least squares
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