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4 marksCorrelation and Linear Regression - Bivariate Data

CAPE Applied Mathematics Unit 1 · 2011 · Paper 2 · Question 5(a)

A table presents the predicted age x and actual age y of ten persons, with summary statistics provided: Σx = 286, Σy = 288, Σxy = 8542, Σx² = 8520, Σy² = 8588.

On the answer sheet provided, draw a scatter diagram of the data in the table.

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Other parts of this question

  1. 5(b)(i)Calculate x̄, the mean of x.[1 mark]
  2. 5(b)(ii)Calculate ȳ, the mean of y.[1 mark]
  3. 5(b)(iii)Plot the point (x̄, ȳ) on the scatter diagram.[2 marks]
  4. 5(c)Calculate the equation of the regression line of y on x and draw this line on the scatter diagram.[7 marks]
  5. 5(d)Calculate the product-moment correlation coefficient r, and interpret the value obtained relative to the scatter diagram.[5 marks]
  6. 5(e)Use your regression line to estimate the actual age of a person whose age was predicted as 45 years.[3 marks]
  7. 5(f)Comment on the reliability of the value obtained in Part (e).[2 marks]

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