Question

CORRELATION COEFFICIENT AND LINEAR REGRESSION Robbie is a food scientist interested in whether bitter flavors, like coffee, become more tolerable as people get older. He sets up a study in which subjects taste cups of coffee with varying intensities. Following is the sample of people used to make the cup he or she liked best. Age (in Years) Grams of Coffee 29 34 48 36 54 37 59 38 60 Independent variable: Dependent variable: у y2 X. y Σ Σ = Σ» Σκ.y=

Answer 1

Solution Independent vanabe : Age. Dependent vanable : Grams of coffee. . 29 34 36 44 48 54 x? 841 1156 1296 y? ху 1936 1276 2304 1632 2916 1944 3481 2183 3600 2280 Ey? 14-237. EXY= 9315 37 59 38 60 1369 1444 Ex? 6106 EX=174 EY- 265 Correlation co-effluent, 'Y' = SSxy SSxx SSyy altershus Ssxy = $xy - [h15xVEY] [5 (174) (265) 9315- = 9315 – 9aa2 93 SSXX Ex?- ElExt] E (174] C106 6106 - 6055.22 50.8

SSyy Ey? I (24) 14237- - [ Caos (2652 14237 14045 13 192. 939 50.9 x 192 93 98.760 0.94167378 ru 0.942. Correlation co Co-efficient r = 0.943 Interpretation :- Y=0.912, means there is a highly positive correlation (ie relationship) between age and gram of coffee which is when Age increap there will be a proportional. increase in grams of coffee *, a= slope, a = H- SSxy SS xx

93 50.8 1.830.708661 aņ 1.831 : ; a = 1.831 ob intercept, be Y-Ra W = sy. 265 8 = EX 174 5. 174 5 Y = 53 34.8 b= 53 - 34.811.831) 53-.63.7188 b= -10.7188 b = -10.719 Equation of regression line = In general, regression line, ŷ - br@x Û -10.719 +1.831 X

Equation of regression line = -10.719+ 1.831(Age) If the person age is 45 year, how many grams Of coffee be will tolerate, Coffee -10.719 +1.831 x 45 -10.719 + 82.395 71.676 be will tolerate . 71..676 grams of coffee, equation, 67 -10.719 +1.831 X 67 +10.719 1.831 S 42.446. ņ 43. of a person can tolerate 67 grams of coffee, what is the age of the person is 43 years. Doctor