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 10 4 6 5 13 6 10 7 15 7 17 8 23 9 19 9 25 10 23 i. Calculate the Σν, Σν, Σε, Σκ? and Σαν (1 mark) ii. Calculate correlation coefficient and interpret its value. (6 marks) iii. 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) vi. Predict the dosage used when the duration of relief is 12 days. (2 marks) v.

pls answer in 4 decimal places

Answer 1

с D E F H X y YA 2 ху 10 100 16 16 (x-x_bar)^2 (y-y_bar)^2 8.41 8.41 3.61 4 5 24 65 25 13 10 36 60 0.81 6 7 15 105 7 (X-X_bar)Y (X-X_bar)y-y_bar) 37.21 -29 17.69 102.01 -17.4 29.29 9.61 -24.7 5.89 37.21 5.49 1.21 1.5 -0.11 0.81 1.7 47.61 25.3 7.59 8.41 39.9 6.09 79.21 52.5 18.69 47.61 71.3 21.39 370.9 9998.1 8998.29 119 36 169 100 225 289 529 361 625 529 2963 17 23 0.01 0.01 1.21 8 184 19 81 171 25 31 225 10 23 230 100 9.61 40.9 517 1223 sum 69 161 16.1 mean 6.9

i) Exi= 161 2412 - 29 63 Exi= 69 Ixi2=517 regress fon equation Y = -2.814 7+2.74088 Exiyi = 1223 V x = 13. ii) corelation coefficient r = n(2x4) - (x) (24) Y = -2.8117+ 2.708 (13) v (nax² (2x)² (n 24 (243² Y - 82.8187 vi spt 12 = 110 1223)-(69*161) J (lom 511) - (695) (60 +2 963) - (1611) 12 = -2.8117 +2.7408X x = 5.4042 r = 0g 102 There is strong positive conelation between X&Y • 110 R²= = 1-ssres SST ssres= 24² ny ? Å, say å i = say Sax SST = Zyl_ny2 È show 824 R².0.8284 variation explained by Porable. iu Bo = 4-8 ix Ŝia Sxy SX4 = Exilxi-x) Sxx = {1xing? Ŝos -2,8117 SXX B = 2.7408