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Time Series & Trend · Question 67 of 68

Question 67

HardOriginal question

For the same output 30, 34, 37, 41 and 48 (2020 to 2024, xx in years from 2022), what is the slope bb of the least-squares trend line?

Options for question 67

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. ∑xy=−60−34+0+41+96=43\sum xy = -60 - 34 + 0 + 41 + 96 = 43 and ∑x2=10\sum x^{2} = 10.

  2. b=4310=4.3b = \frac{43}{10} = 4.3 a year.

Worth noting

8.6 divides by n=5n = 5 instead of ∑x2=10\sum x^{2} = 10; 4.5 is the average yearly rise, first to last.

Concept
The slope by least squares
Typical time
120 s
Your time
—
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.