(2 marks) (c) A quality engineer performed an experiment to study the relationsh
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(2 marks) (c) A quality engineer performed an experiment to study the relationship between a characteristic of paper pulp (measured in Schopper-Riegler degrees) and the hours of beating of the pulp. The results data is listed in Table 6.2 | No. of Hours beating pulp (X variable) I-2T3 4- 5- 6 7-- 8- 10 11 12 13 A characteristic of paper pulp measured 17 21 22 27 36 49 56 64 8086 88 92 94 in Schopper-Riegler degrees (Y variable) Table 6.2: Experimental Results from paper pulp experiment (Ö) (ii) Algebraically determine the line of best fit drawing the line on graph paper (4 marks) (2 marks) Determine the residual when the X variable is 5 hours 0.9697, interpret its precise meaning. Note: Relevant formulae are available on page 9 of the formulae pack (ii) If the co-efficient of determination associated with the line of best fit has been calculated to be 2 marks)Explanation / Answer
X Y x^2 XY 1 17 1 17 2 21 4 42 3 22 9 66 4 27 16 108 5 36 25 180 6 49 36 294 7 56 49 392 8 64 64 512 9 80 81 720 10 86 100 860 11 88 121 968 12 92 144 1104 13 94 169 1222 SUM 91 732 819 6485 The REGRESSION equation is given as Y=a+bX Where a =y bar - b xbar x bar = 91/13= 7 y bar = 732/13=56.31 b=( 6485- 13*7*56.31) / (819)-13(7)^2 b=7.488 a= y bar - b*x bar a=56.31-7.48*7 a=3.95 so equation is given as y=a+bx = 3.95 +7.48 x Answer 2:- when X = 5 y=3.95+7.48*5 y=41.35 Answer:- The coefficient of determiniaton described the level of predictibility. As the value is given as 0.9697 , this indicates that 96.97% of the variance in Y is predictable from X
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