Please show all work and place all answers on this sheet A new drug is designed

Question

Please show all work and place all answers on this sheet A new drug is designed to lower systolic blood pressure. A clinical trial was conducted on a cohort of hypertensiwe patients. The mean dosage of medication used was 25 mgs with a standard deviation of 4 mgs. The mean systolic blood pressure of the treated patients was 125 mm with a stan coefficient was-8 dard deviation of 10 mm. The correlation (a) Construct the equation that predicts (estimates) systolic blood pressure, Y. given medication dosage. x State the equation in the forma+ bx (b) What is the Y-intercept for the equation? What is its interpretation in this context? (c) What is the slope for this equation? What is its interpretation in this context? (d) Estimate the mean blood pressure for an individual who takes 30 mgs of the medication.

Explanation / Answer

SDx= 4mgs , xbar= 25mgs and SDy= 10mm , ybar= 125mm r= -0.8

a) b= r*SDy/SDx = -0.8* 10/4 = -2

b=-2

a= ybar-b*xbar = 125-(-2)*25 = 125+50= 175

a= 175

required equation yhat= a+b*x = 175-2x

yhat= 175-2x

b) Y intercept of the equation is 175 . It is positive.

c) slope for this equation = b=-2

Interpretation: systolic blood pressure is expected to decrease by 2mmHg on average per 1mg increase in drug dosage.

d) Estimated mean blood pressure for 30mgs of the medication

yhat= 175-2*30= 175-60=115

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