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4 marksCorrelation and Linear Regression - Bivariate Data

CAPE Applied Mathematics Unit 1 · 2008 · Paper 2 · Question 6(a)

Masses x (in kg) and heights y (in cm) of a sample of 8 adults are given along with summary statistics.

On the answer sheet provided, plot a scatter diagram for the data.

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Other parts of this question

  1. 6(b)(i)Calculate the product-moment correlation coefficient, r, for these data.[2 marks]
  2. 6(b)(ii)Interpret the value obtained for r.[2 marks]
  3. 6(c)(i)Calculate (\bar{x}, \bar{y}), where \bar{x} is the mean of x and \bar{y} is the mean of y.[3 marks]
  4. 6(c)(ii)Plot the coordinates (\bar{x}, \bar{y}) on the scatter diagram.[1 mark]
  5. 6(d)(i)Derive the equation of the regression line y on x in the form y = a + bx.[5 marks]
  6. 6(d)(ii)Plot this regression line on the scatter diagram.[2 marks]
  7. 6(e)Use your regression line y on x to estimate the height of an adult whose mass is 60 kg.[2 marks]
  8. 6(f)The regression line y on x is used to estimate the height of an adult whose mass is 82 kg. Giving a reason for your answer, state whether such an estimate…[2 marks]
  9. 6(g)Giving a reason for your answer, state which one of the regression lines, y on x OR x on y, should be used to estimate the mass of an adult whose height is 156…[2 marks]

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