RI 2025 H2 S6 Corr and Reg Tutorial Qns

RAFFLES INSTITUTION H2 Mathematics 9758 2025 Year 6 _______________________________ Tutorial S6: Correlation and Regression Page 1 of 6 Tutorial S6: Correlation and Regression 1 The amounts, x grams, of catalyst used in a chemical reaction and the resulting times, y hours, taken to complete the reaction were recorded. The results are given in the following table. x 2.0 2.5 3.0 3.5 4.0 4.5 5.0 y 62.1 51.2 44.1 39.2 35.0 37.3 33.0 (i) Calculate the value of the product moment correlation coefficient for the data. (ii) State what your value indicates about the relation between x and y, and what you expect about the scatter diagram from this sample. (iii) Draw a scatter diagram of the data and comment on your answer to part (ii). [(i) 0.925 ] 2 The variables x and y are believed to be linearly related and a set of values of x and y are obtained experimentally. Both variables are subject to experimental error. State circumstances under which the regression line of x on y should be used, rather than the regression line of y on x, when the value of one variable is to be estimated from a given value of the other. The heart rate (x) and diastolic blood pressure (y), both in suitable units, were measured for each of 10 hospital patients after being given a certain drug. The results were as follows. x 49 51 54 58 63 64 68 70 75 78 y 90 88 85 91 82 85 76 77 70 71 (i) By referring to the scatter diagram of the data obtained using your graphing calculator, state what the scatter diagram indicates about the correlation between x and y. (ii) Calculate the equation of the estimated least square regression line of y on x in the form y a bx  , giving the values of a and b correct to 3 significant figures. (iii) Use a suitable regression line to estimate the heart rate when the diastolic blood pressure is 80. Give a reason why it might be unwise to use either of the regression lines to estimate the diastolic blood pressure when the heart rate is 90. (iv) Find the product moment correlation coefficient for the data and state, giving a reason, whether its value confirms your statement in part (i). [ (ii) 126 0.704y x  (iii) 64.8 (iv) 0.919 ]

Raffles Institution H2 Mathematics 2025 Year 6 _____________________________________________________________________________________________ ________________________________ Tutorial S6: Correlation and Regression Page 2 of 6 3 The following data is collected from a trial of a weedkiller. Trial field areas, each of area 1 hectare, were treated with different volumes of weedkiller. The volume of weedkiller applied is v litres, and x is the number of weeds found in the corresponding hectare after the weedkiller is applied. (i) Calculate the equation of the regression line of x on v in the form x a bv  . (ii) Use your answer to estimate the number of weeds that would be found in an area of 1 hectare t