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

CAIE FP2 2013 June Q6
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
  1. (a) 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 \({ } ^ { - } 0.4\).
      (b) 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)
    3. A histogram was drawn to show the distribution of age in completed years of the participants on an outward-bound course.
    There were 32 people aged 30-34 years on the course. The height of the rectangle representing this group was 19.2 cm and it was 1 cm in width. Given that there were 28 people aged 35-39 years,
    (a) find the height of the rectangle representing this group. Given that the height of the rectangle representing people aged 40-59 years was 2.7 cm ,
    (b) find the number of people on the course in this age group.