By Arthur H. Hall (auth.)

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Plot the scattergram for each of the following bivariate distributions. (i) X 8 10 12 16 20 22 27 25 19 15 13 y 15 16 21 24 23 24 26 26 25 22 20 X (ii) (iii) y X y X y 30 34 36 27 26 26 0 3 5 7 3 4 6 8 0 20 30 60 46 40 38 40 42 24 25 23 10 13 15 9 10 12 38 60 70 39 26 16 44 46 23 21 20 26 17 20 14 15 82 100 13 0 28 27 32 25 Comment on the differences in the three scattergrams. Find the centroid and regression equation for each of the last two. 56 4. Tests were made on fifteen brands of cigarettes to ascertain the tar and nicotine yield in mg per cigarette.

500 ± 10)- (350 ± 20) + (60 ± 5) = (500- 350 + 60) ± (10 + 20 + 5) = 210±35 The expected answer is 210. The absolute error is 35. The answer lies in the range 175 to 245. The relative error of the answer is (35/210) x 100 = 16~ per cent. e. AB + ab and the absolute error aB + Ab Quite frequently the errors a and b are so small that ab is negligible and can be ignored in comparison with AB, so the answer is given as AB ± (aB + Ab} (500 ± 10} X (200 ± 5} = 100000 ± (2000 + 2500} +50 = 100000 ± 4500 ignoring the 50 Division The maximum and minimum possible answers are (A+ a}/(B- b) and (A- a}/(B +b).

E. with values= x) belong to neither group. The centroids Land Rare calculated for the left-hand and right-hand groups respectively. We have now three points G, L, R and these are used in the 'three-point' method to determine the line of best fit as shown in the following example. 5 Example Plot the scattergram for the data and draw the regression line (line of best fit) using the three-point method. e. the equation of the regression line). X y 0 0 2 2 4 4 8 6 4 2 8 8 5 4 12 4 12 6 14 4 16 5 18 8 The student should plot the points himself and follow the working through on his own graph, comparing it with Fig.