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2 marksCorrelation and Linear Regression - Bivariate Data

CAPE Applied Mathematics Unit 1 · 2014 · Paper 2 · Question 6(b)(ii)

Aptitude test scores x and performance scores y for 10 workers are summarized: sum(x) = 377, sum(y) = 297, sum(xy) = 11305, sum(x^2) = 14397, sum(y^2) = 9145.

Estimate the performance score for a person whose aptitude score was 37.

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  1. 6(a)(i)State the null and alternative hypotheses for this test.[2 marks]
  2. 6(a)(ii)a)Determine the number of degrees of freedom for the test.[2 marks]
  3. 6(a)(ii)b)Determine the critical region for the test.[2 marks]
  4. 6(a)(iii)Determine the expected frequency for the cell in the third row and second column (observed count 15).[2 marks]
  5. 6(a)(iv)The calculated chi-square test statistic is 9.1625. State the conclusion of the test.[2 marks]
  6. 6(b)(i)Obtain the regression equation of y on x in the form y = a + bx.[6 marks]
  7. 6(b)(iii)Interpret the regression coefficient b in the context of the problem.[2 marks]
  8. 6(b)(iv)Calculate the product-moment correlation coefficient, r, and interpret its value.[5 marks]

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