RI S6 Corr and Reg_Add Prac_Qns

RAFFLES INSTITUTION H2 Mathematics 9758 2025 Year 6 Additional Practice Questions for Chapter S6: Correlation and Regression 1 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] 2 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 data as shown in your calculator. [2] (ii) Find x and ,y and mark the point  ,x y on your scatter diagram. [2] (iii) Calculate the equation of the regression line of y on x, and draw this line on your scatter diagram. [2] (iv) Calculate the product moment correlation, and comment on its value in relation to your scatter diagram. [2] (v) For the next three-month period, the sales target is 20 cranes. Estimate the corresponding profit. [2] (vi) The company’s sales director uses the regression line in (iii) to predict the profit if 40 cranes were to be sold in a three-month period. Comment on the validity of this prediction. [2] x 15 17 13 21 16 22 14 18 y 290 350 270 430 340 410 300 360

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ ______________________________________________________ Additional Practice Questions for Chapter S6: Correlation and Regression Page 2 of 7 3 Explain why it is advisable to draw a scatter diagram before interpreting a correlation coefficient calculated for a sample drawn from a bivariate distribution. [1] Sketch a scatter diagram that shows an obvious relation between two variables but which yields a linear product-moment correlation coefficient that is close to zero. [1] 4 A medical officer wishes to investigate a patient’s heart-beat rate h beats per minute (bpm) when he walks at different speeds s km/h. The data is shown below: s (km/h) 1 1.5 2 2.5 3 3.5 4 4.5 5 h (bpm) 60 63 66 75 86 99 150 110