EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Time Series & Trend · Question 61 of 68

Fitting a straight-line trend by least squares, with x = 0 at 2022 and x in years, what is the slope of the…

Question 61

MediumOriginal question

A dealer's scooter sales, in hundreds, were 42, 45, 51, 54 and 60 in the five years 2020 to 2024.

Fitting a straight-line trend by least squares, with x=0x = 0 at 2022 and xx in years, what is the slope of the dealer's trend?

Options for question 61

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. x=−2,−1,0,1,2x = -2, -1, 0, 1, 2: ∑xy=−84−45+0+54+120=45\sum xy = -84 - 45 + 0 + 54 + 120 = 45 and ∑x2=10\sum x^{2} = 10.

  2. b=∑xy∑x2=4510=4.5b = \frac{\sum xy}{\sum x^{2}} = \frac{45}{10} = 4.5.

Worth noting

45 is ∑xy\sum xy before dividing by ∑x2=10\sum x^{2} = 10.

Concept
The least-squares slope
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.