Question

In University of Harimau Malaya, Dr Ku is doing a research in developing a new drug for an allergy. He conducts an experiment to study how different dosages of the drug affect the duration of relief from the allergic symptoms. There are ten patients are included in the experiment. Each patient receives a specified dosage of the drug and asked to report back as soon as the protection of the drug seems to wear off. The observations are recorded in table below, which shows the dosage (in Milligrams) and duration of relief (in Days) for the 10 patients. Duration of Dosage, x Relief, y 4 4 5 6 7 7 8 9 9 10 10 6 13 10 15 17 23 19 25 23 111. i. Calculate the y Ey. Ex. Ex and Exy (1 mark) ii. Calculate correlation coefficient and interpret its value. (6 marks) Calculate coefficient of determination and interpret its value. (2 marks) iv. Estimate the regression parameters and write the estimated linear regression model. (7 marks) Predict the duration of relief when the dosage 13 mg. (2 marks) Predict the dosage used when the duration of relief is 12 days. (2 marks) V. vi.

Answer 1

i. I ; = 10+6+13+0+15+17+23+19+25+23 = 161 y = 102+62+12+102 +152 +172423P+19+25+232 - 2963. 2 I ai= = 4+4+5+6+7+7+ 8+9+9+10 -69. = 42+4+52 +62+72472482492492 102-517. pey; = (4x10)+(4X6) +(5X13) +(6x10) +3X15) +6X17) +(8X23) +9x19) + (9X25) + 10X23) = 1223 ne number of observations of ze ory n = 10 formula for correlation coefficient r i ran [Xi9; Σα Συ; [1 2x2 - (322;)?] [n Zy?- (24;)?] 20 x 1223) - (69X161) [(20x517) – 69²] [ 20x 2963) – 1612] r = 0.9101554 Value of correlation coefficient near to i implies that there is a perfect positive linear relationship between x and Y. so, r= 0.9101554 can be interpreted as, there is strong positive linear relationship between Dosage and duration of relief lie. more the dosage more duration of relief. a is the

iii. So coefficient of determination is the square of the correlation coefficient. coefficient of dekrmination is (0.9101552) ?= 0.8283828 Coefficient of determination is interpreted is interpreted as the amount of Variation in Y explained by Xi 82.83828 % of variation in the data on duration of relief is explained by the data on dosage. SO, iv. In general, the estimated linear regression model is ŷi = Rot Razi Bo and B are estimated regression parameters. BA Taigi - ne ; Bou ý - paz [x²nze 2 ł = [Xi and 3 - 2s; n T= 69 6.9 and = 161 162 10 161 :. És = 1223 -(1046-9x1611) (51.1 - 30x692) E 217408313. 1. Po = 5-pix = 16:1-(2.7408813 X 6.9) = -2.811736 :'. B2 = 2.7408313 and Bo = -2.811736 estimated linear regression model is 1 Yi = -2,811736 + 2.7408813 Dj

V. To predict the duration of relief when the dosage 13 just substitute X=13 in the above regression equation and obtain the value of Y - Yi : -2.811736 +(2-7408813 x 13). 1 324 8190709 & こ I AL Duration of relief is 38 days Gapproximately) when the dosage is 13 mj. Vi. To predict the dosage used when the duration of relief is 12 days just put ŷi = 12 and obtain the corrosponding &; using above regression equation. 12- 2-811736 +(2.7408313 X 2i) 12+2-811 736 = (2.7408313 x Bli) 14.811736 217408313 Oli = 5.40410349. Dosage used is 5:40410349 mg when the duration of is 12 days. relief

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