RI S6 Corr and Reg_Add Prac_Solns

RAFFLES INSTITUTION H2 Mathematics 9758 2025 Year 6 _______________________________________________________ Additional Practice Questions for Chapter S6: Correlation and Regression Page 1 of 18 Additional Practice Questions for Chapter S6: Correlation and Regression (Solution) 1 8863/2007/01/Q8 Seven cities in a certain country are linked by rail to the capital city. The table below shows the distance of each city from the capital and the rail fare from the city to the capital. City A B C D E F G Distance, x km 124 44 76 148 16 180 104 Rail fare, $y 156 53 99 169 23 177 138 (i) Give a sketch of the scatter diagram for the data as shown on your calculator. [2] (ii) Calculate the product moment correlation coefficient. [1] You are given that the regression line of y on x has equation 16.7 1.01y x  , where the coefficients are given correct to 3 significant figures. (iii) Calculate the equation of the regression line of x on y, giving your answer in the form x a by  . [1] (iv) Use the appropriate regression line to estimate (a) the rail fare from a city that is 28 km from the capital, [2] (b) the distance of a city from the capital if the rail fare is $198. [2] (v) Comment briefly on the reliability of the estimates in part (iv). [2] [ (ii) 0.973 (3sf)r (iii) 10.6 0.940 (3sf)x y  (iv)(a) $45 (b) 176 km ] Solution: (i) (iv) (a) Given 28x , use the regression line of y on x to get 44.98 45 (nearest integer)y  . So the estimated rail fare is $45. (iv) (b) Given 198y , use the regression line of x on y , i.e. 10.558 0.93976x y  (5s.f) to get 176x (3s.f.). So the estimated distance is 176 km. (v) The value 28x is within the given range of values of x where 16 180x  . Since interpolation was used, and the correlation coefficient 0.973 is close to 1, indicating a strong positive linear correlation between the variables, the estimate obtained in (a) is likely to be reliable. The value 198y is beyond the given range of values of y where 23 177y  . Since extrapolation was used, the estimate obtained in (b) is unlikely to be reliable. 177 23 16 180 x y (ii) 0.973 (3sf)r (iii) 10.6 0.940 (3sf)x y  10.558 0.93976 (5sf)x y 

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ _______________________________________________________ Additional Practice Questions for Chapter S6: Correlation and Regression Page 2 of 18 2 8863/2008/01/Q11 An engineering company makes cranes. The numbers, x, sold in each three-month period for two years, together with the profits, y thousand dollars, on the sale of these cranes are given in the following table. (i) Give a sketch of the scatter diagram for the