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2 marksCorrelation and Linear Regression - Bivariate Data

CAPE Applied Mathematics Unit 1 · 2013 · Paper 2 · Question 6(a)(ii)

Profit y (dollars per sales dollar) on 9 projects and foreman experience x (years) follow the regression equation y = 6.6 + 0.09x.

Interpret the value of 6.6 in this equation.

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  1. 6(a)(i)Interpret the value of 0.09 in this equation.[2 marks]
  2. 6(a)(iii)Use the regression equation to estimate the value of y when x = 15.[2 marks]
  3. 6(a)(iv)The product moment correlation coefficient for the data is 0.32. Interpret this value relative to the variables x and y.[2 marks]
  4. 6(b)(i)State appropriate null and alternative hypotheses for this test.[2 marks]
  5. 6(b)(ii)Copy and complete the table of observed (O) and expected (E) frequencies of the grades obtained in the examination.[4 marks]
  6. 6(b)(iii)a)Determine the number of degrees of freedom for this hypothesis test.[2 marks]
  7. 6(b)(iii)b)Determine the critical region of the test.[2 marks]
  8. 6(b)(iii)c)Calculate the χ² test statistic.[5 marks]
  9. 6(b)(iv)Clearly state the conclusion which may be drawn from this test.[2 marks]

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