Sketch theoretical scatter diagram

Question asks the student to sketch a scatter diagram that would illustrate a specified correlation coefficient or theoretical relationship, without providing actual data.

2 questions · Moderate -0.8

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CAIE FP2 2013 June Q6
6 marks Moderate -0.8
6 Six pairs of values of variables \(x\) and \(y\) are measured. Draw a sketch of a possible scatter diagram of the data for each of the following cases:
  1. the product moment correlation coefficient is approximately zero;
  2. the product moment correlation coefficient is exactly - 1 . On your diagram for part (i), sketch the regression line of \(y\) on \(x\) and the regression line of \(x\) on \(y\), labelling each line. On your diagram for part (ii), sketch the regression line of \(y\) on \(x\) and state its relationship to the regression line of \(x\) on \(y\).
Edexcel S1 Q1
6 marks Moderate -0.8
  1. Draw two separate scatter diagrams, each with eight points, to illustrate the relationship between \(x\) and \(y\) in the cases where they have a product moment correlation coefficient equal to
    1. exactly \(+1\),
    2. about \(-0.4\). [4 marks]
  2. Explain briefly how the conclusion you would draw from a product moment correlation coefficient of \(+0.3\) would vary according to the number of pairs of data used in its calculation. [2 marks]