Question

2) The volume (in cm?) and the temperature (in C) of a gas were recorded each minute for 12 minutes while the gas was heated. The data collected is shown below: Volume (cm) 100 102 105 108 Temperature (°C) 18.0 18.5 19.1 19.8 20.6 22.5 23.6 25.2 27.0 29.2 113 116 120 124 127 130 a) Find the equation of the regression line in the form y = a + bx. Use two decimal places in your calculations of a and b. (8 marks) b) Explain the practical significance of the values of a and b. (2 marks) c) Estimate the volume of the gas when the temperature is 10 °C and state whether the estimate is reliable. (2 marks) (Total 12 marks]

Answer 1

Clearly, independent variable is . temparature Dependent (y) is variable volume yz XxY x2 x Y 10,000 324 18 OO Ils.o 10o 10,404 342ias 102 p 8 8 7 is.s 11,on's 2oos.5 364.81 105 19.1 llo 664 2138.4 392.04 108 19.8 12,769 113 2 3 27.& 424-36 2006 13,456 50 6.25 2 6 16 116 22.5 55 bo95 141400 2 & 3 ? 1 2 23.6 635.04 151376 312 4.8 124 25.2 16,129 729 9429 127 802.64 State35 16 900 3796 29,2 130 5127.35 13,21123 Sumz 223.5 25950.5 1145

X Exi 1 aa.35 22 3.5 sohli Z Yi 1145 To ssxx Exi? - 5 (Exi) D23:57 5127.35 132.175 2 Evi) Eye- 3 syy 1145? 137123 10 102.5 s sxy - Exiv; - < (3x) (sv) +*23.5) (145) 25950.5-

be ss XY ss xx 35 9.75 132, POE Q. 228 Y-X.b az 114.5 2 ੨ · ਜੋ ੨ ੨੬ Q2- 35 5 3.6454 of (6) The practical significance of the slope the b is practreal lino The regression of the al is significance the value when Y of of zero is value x

estimated the anen res x z10, bel volume will У at bolo 53.645 ut 2-7 2 28.*lo 80.8 3 3 2 coefficient, The correlation s sxy 6 Josxx ssyy 359.75 132.1QS X 1020.5 O. 979 of determination The coefficient Ree əz 0.9599 of ied. variation is explaind of 95.90% the estimated value is reliable, by a. Hence,