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5 marksCorrelation and Linear Regression - Bivariate Data

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

Data for distance x (km) and travel time y (minutes) for 9 conference delegates are recorded with summary statistics: sum(x) = 850, sum(y) = 1076, sum(x^2) = 93682, sum(xy) = 117841, sum(y^2) = 153776.

Plot the scatter diagram for the distance and travel time data on the provided answer sheet.

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Other parts of this question

  1. 6(b)Calculate and interpret the product-moment correlation coefficient between distance and travel time.[5 marks]
  2. 6(c)(i)Find the equation of the regression line of y on x in the form y = a + bx.[4 marks]
  3. 6(c)(ii)Draw the regression line on the scatter diagram.[3 marks]
  4. 6(d)(i)Interpret the value of the regression coefficient b in the context of the problem.[1.5 marks]
  5. 6(d)(ii)Interpret the value of the constant a in the context of the problem.[1.5 marks]
  6. 6(e)(i)Estimate the travel time for a delegate who travelled 145 km by car.[3 marks]
  7. 6(e)(ii)Comment briefly on the reliability of the estimated travel time.[2 marks]

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