Further Mathematics · Pearson Edexcel 9FM0 · Option FS2 · Topic 1

Linear regression

Fitting a least squares regression line and checking it with residuals.

  • 2 sub-topics
  • Taught in Year 13
  • 41 practice questions
  • 2 animated lessons
Practice questions (41) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 1.1Least squares linear regressionY13
  2. 1.2ResidualsY13

Try 2 questions

Easy and medium questions from this topic, each with a worked solutions and the mark for every step. All 41 questions in this topic, free, no account needed.

Linear regression

Not needed for Year 12Easy

The gradient of a regression line · Year 13 · 1 mark

  1. For a set of data, Sxy=45S_{xy} = 45 and Sxx=25S_{xx} = 25. What is the gradient of the regression line of yy on xx?
    (1)

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  1. b=SxySxxb = \dfrac{S_{xy}}{S_{xx}}.CC: 1.8

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Linear regression

Not needed for Year 12Medium

Least squares regression · Year 13 · 6 marks

For 12 pairs of data on temperature, xx °C, and a reaction time, yy seconds: ∑x\sum x=263, ∑y{}= 263, \ \sum y=−182.6, ∑x2{}= -182.6, \ \sum x^2=6947, ∑xy{}= 6947, \ \sum xy=−6858.2{}= -6858.2.
  1. (a)
    Find the equation of the regression line of yy on xx.
    (4)
  2. (b)
    Use your equation to estimate yy when x=23x = 23, and comment on the reliability of estimating yy when x=61x = 61.
    (2)
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Part (a)4 marks

  1. SxxS_{xx}=6947−263212{}= 6947 - \frac{263^2}{12}=1182.9, Sxy{}= 1182.9, \ S_{xy}=−6858.2{}= -6858.2−263×−182.612{}- \frac{263 \times -182.6}{12}=−2856.2{}= -2856.2
  2. b=SxySxx=−2.415b = \frac{S_{xy}}{S_{xx}} = -2.415
  3. a = ȳ − b x̄.y=37.70−2.415xy = 37.70 - 2.415x

Part (b)2 marks

  1. y≈−17.8y \approx -17.8
  2. x=61x = 61 is outside the range of the data (extrapolation), so that estimate is unreliable.

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