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Correlation and Linear Regression - Bivariate Data · CAPE Applied Mathematics Unit 1

61 past-paper questions on Correlation and Linear Regression - Bivariate Data, part of Module 3: Analysing and Interpreting Data, from every CAPE Applied Mathematics Unit 1 paper on Quelpr.

Practise Correlation and Linear Regression - Bivariate Data
  1. 6(a)4 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2On the answer sheet provided, plot a scatter diagram for the data.
  2. 6(b)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Calculate the product-moment correlation coefficient, r, for these data.
  3. 6(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Interpret the value obtained for r.
  4. 6(c)(ii)1 mark· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Plot the coordinates (\bar{x}, \bar{y}) on the scatter diagram.
  5. 6(d)(i)5 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Derive the equation of the regression line y on x in the form y = a + bx.
  6. 6(d)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Plot this regression line on the scatter diagram.
  7. 6(e)2 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Use your regression line y on x to estimate the height of an adult whose mass is 60 kg.
  8. 6(f)2 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2The 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 would be reliable.
  9. 6(g)2 marks· CAPE Applied Mathematics Unit 1 · 2008 · Paper 2Giving 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 cm.
  10. 6(a)5 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Plot the scatter diagram for the distance and travel time data on the provided answer sheet.
  11. 6(b)5 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Calculate and interpret the product-moment correlation coefficient between distance and travel time.
  12. 6(c)(i)4 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Find the equation of the regression line of y on x in the form y = a + bx.
  13. 6(c)(ii)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Draw the regression line on the scatter diagram.
  14. 6(d)(i)1.5 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Interpret the value of the regression coefficient b in the context of the problem.
  15. 6(d)(ii)1.5 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Interpret the value of the constant a in the context of the problem.
  16. 6(e)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Estimate the travel time for a delegate who travelled 145 km by car.
  17. 6(e)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2008 (second paper) · Paper 2Comment briefly on the reliability of the estimated travel time.
  18. 6(b)5 marks· CAPE Applied Mathematics Unit 1 · 2009 (second paper) · Paper 2It is found that the regression line of y on x passes through the point (0, 2). If the means of the x and y values are 6 and 8 respectively, find the equation of the regression line of y on x and express it in the form…
  19. 5(a)4 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2On the answer sheet provided, draw a scatter diagram of the data in the table.
  20. 5(b)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Plot the point (x̄, ȳ) on the scatter diagram.
  21. 5(c)7 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate the equation of the regression line of y on x and draw this line on the scatter diagram.
  22. 5(d)5 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Calculate the product-moment correlation coefficient r, and interpret the value obtained relative to the scatter diagram.
  23. 5(e)3 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Use your regression line to estimate the actual age of a person whose age was predicted as 45 years.
  24. 5(f)2 marks· CAPE Applied Mathematics Unit 1 · 2011 · Paper 2Comment on the reliability of the value obtained in Part (e).
  25. 6(b)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2On the graph sheet provided, plot these values as a scatter diagram.
  26. 6(b)(ii)a)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Interpret the value 0.8 in the regression equation as it relates to the rainfall at the two stations.
  27. 6(b)(ii)c)3 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Draw the regression line y = 0.8x + 0.38 on the same graph as the scatter diagram.
  28. 6(b)(ii)d)2 marks· CAPE Applied Mathematics Unit 1 · 2012 · Paper 2Use the regression line to estimate the rainfall at Station B when the rainfall at Station A is 4.5 cm.
  29. 6(a)(i)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Interpret the value of 0.09 in this equation.
  30. 6(a)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Interpret the value of 6.6 in this equation.
  31. 6(a)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2Use the regression equation to estimate the value of y when x = 15.
  32. 6(a)(iv)2 marks· CAPE Applied Mathematics Unit 1 · 2013 · Paper 2The product moment correlation coefficient for the data is 0.32. Interpret this value relative to the variables x and y.
  33. Q331 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1Which of the following values for the product-moment correlation coefficient, r, indicates the strongest degree of linear correlation between the two variables?
  34. Q341 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The regression line y on x
  35. Q371 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2014 · Paper 1The time, x minutes, taken on 9 different occasions for an air conditioning unit to reach its desired temperature, y\ ^\circ\text{C}, when switched on is summarized by \sum x = 68.8, \sum x^2 = 753.9, \sum y =…
  36. 6(b)(i)6 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Obtain the regression equation of y on x in the form y = a + bx.
  37. 6(b)(ii)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Estimate the performance score for a person whose aptitude score was 37.
  38. 6(b)(iii)2 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Interpret the regression coefficient b in the context of the problem.
  39. 6(b)(iv)5 marks· CAPE Applied Mathematics Unit 1 · 2014 · Paper 2Calculate the product-moment correlation coefficient, r, and interpret its value.
  40. 6(a)(i)1 mark· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Identify the independent variable between: The income of a family, and The monthly rent paid.
  41. 6(a)(ii)1 mark· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Identify the independent variable between: The advertising expense of a company, and The sales of a company.
  42. 6(a)(iii)1 mark· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Identify the independent variable between: The damage done to a certain home after a hurricane, and The amount of money spent in repairs to a certain home after a hurricane.
  43. 6(b)(i)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Use graph paper to plot these values in a scatter diagram.
  44. 6(b)(iii)1 mark· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Plot the point (x̄, ȳ) on the scatter diagram.
  45. 6(b)(iv)3 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Draw the regression line of y on x given by y = -0.05 + 0.27x on the same graph as the scatter diagram.
  46. 6(b)(v)2 marks· CAPE Applied Mathematics Unit 1 · 2015 · Paper 2Use the regression line to estimate the number of days required to train a new operator aged 22 years, to the NEAREST whole number.
  47. Q371 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2016 · Paper 1The time, x minutes, taken on 9 different occasions for an air conditioning unit to reach its desired temperature, y\ ^\circ\text{C}, when switched on is summarized by $\sum x = 68.8, \sum x^2 = 753.9, \sum y =…
  48. Q351 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1Item 35 refers to the following scatter diagram. The product-moment correlation coefficient of the data shown is
  49. Q371 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1The time, x minutes, taken for an air conditioning unit to reach its desired temperature, y\ ^\circ\text{C}, when switched on on 9 different occasions is summarized by \Sigma x = 68.8, \Sigma x^2 = 753.9,…
  50. Q411 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1The regression line of y on x passes through the point (0, 2). The means of x and y are 6 and 8 respectively. The equation of the regression line is
  51. Q421 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2017 · Paper 1The regression line y = 0.95x + 0.4 provides a linear model for the cost, y hundred dollars, associated with producing x components. What is the practical interpretation of the coefficient 0.95?
  52. Q211 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1Which of the following scatter diagrams shows negligible correlation?
  53. Q361 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1If the product-moment correlation coefficient between a person's weight and annual income is 0.9, it could be concluded that
  54. Q391 mark · multiple choice· CAPE Applied Mathematics Unit 1 · 2018 · Paper 1The regression line y on x
  55. 6(a)4 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Calculate the gradient of the regression line y on x.
  56. 6(b)4 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Calculate the intercept of the regression line.
  57. 6(c)2 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Interpret the value of the gradient in the context of the data.
  58. 6(d)2 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Using the obtained regression equation (y = a + bx), determine the score of an athlete who trained 64 hours for the competition.
  59. 6(e)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Calculate the correlation coefficient.
  60. 6(f)3 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2Interpret the value of the correlation coefficient calculated in (e).
  61. 6(g)7 marks· CAPE Applied Mathematics Unit 1 · 2022 · Paper 2On the grid provided on page 27, plot a scatter diagram to represent the information in the table. Draw the regression line on the same grid.

Related topics in Module 3: Analysing and Interpreting Data