Mathematics 301 Quis as November 16, 2017 Please show all work and place all ans

Question

Mathematics 301 Quis as November 16, 2017 Please show all work and place all answers on this sheet A new drug is designed to lower systolic blood pressure. A clinical srial was comdbacted on patients The with a standard deviation of 4 me-Th·mean yt (a) Construct the equation that predicts (estimates) systolic blood pressure, Y V given medication dosage, x State the equation in the form ma + (b) What is the Y-intercept for the equation? What is its interpretation in this contex (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

Here x = 25 mgs

sx = 4 mgs

ybar = 125 mm

sy   = 10 mm

here ,

correlation coefficient r = - 0.8

(a) Here, if linear regression line

y^ = a + bx

then, b = r Sy / Sx = (-0.8) * (10/4) = -2 mm/ mgs

now this line will pass through the mean point

a = 125 + 2 * 25 = 175 mm

y^ = 175 - 2x

(b) Here, the y - intercept here is 175 mm that means here that if there is no dosages given to the patient then his/her systoic blood pressure would be predicted equal to 175 mm.

(c) Here slope is -2 mm/mgs that means if we increase the dose of drug by 1 mgs that will reduce the systolic blood pressure by 2 mm.

(d) Here if X = 30 mgs

y^ = 175 - 30 * 2 = 115 mg.

(e) Here r = -0.8

R2 = 0.64

so 64% of variation is explained by variability in medicataion.

(f) Here x = 30 mg

y^ = 175 - 30 *2 = 115 mg

sy l x = 30 = 10 * sqrt(1 - 0.82) = 6

so Y (y < 130 mg l x = 30 mg ) = NORM (y < 130 mg ; 115 mg ; 6mg )

Z = (130 - 115)/6 = 2.5

Y (y < 130 mg l x = 30 mg ) = NORM (y < 130 mg ; 115 mg ; 6mg ) = Pr( Z< 2.5) = 0.9938

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