Further Mathematics · OCR H245 · Option S · Topic 5.09

Linear regression

Dependent and independent variables, calculation of the equation of the regression line, use of the regression line.

  • 3 sub-topics
  • Taught in Year 13
  • 46 practice questions
  • 3 animated lessons
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What the specification says

Every sub-topic OCR 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. 5.09aDependent and independent variablesY13
  2. 5.09b-dCalculation of the equation of the regression lineY13
  3. 5.09eUse of the regression lineY13

Try 2 questions

Easy and medium questions from this topic, each with a worked solutions and the mark for every step. All 46 questions in this topic, free, no account needed.

Linear regression

Easy

Independent and dependent variables · Year 12 · 1 mark

  1. In an experiment, the dose is set at chosen values and the fall in blood pressure is measured. Which is the independent (controlled) variable?
    (1)

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  1. The independent variable is the one whose values the experimenter chooses. The dependent (response) variable is then measured.A: The dose of a drug

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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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