The following data were collected on a simple random sample of 12 patients with hypertension. The variables are:

Y = mean arterial blood pressure (mm Hg) X₁ = age ( years ) X₂ = weight ( kg) X₃ = body surface area ( sq m) X₄ = duration of hypertension ( years ) X₅ = Basal pulse ( beats/min) X₆ = Measure of stress

Patient	Y	X1	X2	X3	X4	X5	X6
1 2 3 4 5 6 7 8 9 10 11 12	105 115 116 117 112 121 121 110 110 114 114 115	47 49 49 50 51 48 49 47 49 48 47 49	85.4 94.2 95.3 94.7 89.4 99.5 99.8 90.9 89.2 92.7 94.4 94.1	1.75 2.10 1.98 2.01 1.89 2.25 1.90 2.25 1.83 2.07 2.07 1.98	5.1 3.8 8.2 5.8 7.0 9.3 6.2 2.5 7.1 5.6 5.3 5.6	63 70 72 73 72 71 66 69 69 64 74 71	33 14 10 99 95 10 42 62 62 35 90 21

For the above data

(i) Fit a linear multiple regression of Y on the independent variables and test for significance of the model at 5% level of significance.

(ii) Test the significance of the partial regression coefficient of mean arterial blood pressure on body surface area.

(iii) Predict the value of mean arterial blood pressure of a patient aged 50 years, weighing 90 kg, with a body surface area of 1.93 sq m, base pulse beat of 75 beats/min and having hypertension for the last 8 years with a stress value of 35 andobtain the corresponding 95% prediction interval.

(iv) Obtain the values of multiple correlation coefficient of Y on the rest of the independent variables and also the multiple coefficient of determination.

(v) Obtain the value of partial correlation coefficient between mean arterial blood pressure and body surface area controlling for other independent variables and test for its significance.