A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the Minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in Millimeters of mercury (mmHg), for a sample of eight adults. The following table presents the
Results.
$\begin{array} { c c }
\text { Systolic } & \text { Diastolic } \
127 & 92 \
125 & 94 \
135 & 87 \
110 & 75 \
123 & 89 \
121 & 87 \
118 & 87 \
127 & 93
\end{array}$
The least-squares regression equation is $y = 18.7841 + 0.5616 x$ . If the systolic pressures of two patients Differ by 8 mmHg, by how much would you predict their diastolic pressures to differ?
A) 8.56 mmHg
B) 4.49 mmHg
C) 0.56 mmHg
D) 0.07 mmHg

Question

A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the Minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in Millimeters of mercury (mmHg), for a sample of eight adults. The following table presents the
Results. 
$\begin{array} { c c } 
\text { Systolic } & \text { Diastolic } \
127 & 92 \
125 & 94 \
135 & 87 \
110 & 75 \
123 & 89 \
121 & 87 \
118 & 87 \
127 & 93
\end{array}$
 The least-squares regression equation is $y = 18.7841 + 0.5616 x$ . If the systolic pressures of two patients Differ by 8 mmHg, by how much would you predict their diastolic pressures to differ?
A) 8.56 mmHg
B) 4.49 mmHg
C) 0.56 mmHg
D) 0.07 mmHg

Quizplus · Accepted Answer

We can use the regression equation to predict the diastolic pressure for each systolic pressure:

For the first patient, with systolic pressure x1, the predicted diastolic pressure is:
y1 = 18.7841 + 0.5616(x1)

For the second patient, with systolic pressure x2 = x1 + 8, the predicted diastolic pressure is:
y2 = 18.7841 + 0.5616(x2) = 18.7841 + 0.5616(x1 + 8)

Now we can calculate the difference between the predicted diastolic pressures:
y2 - y1 = 0.5616(x1 + 8) - 0.5616x1 = 0.5616(8) = 4.49

Therefore, we predict that the diastolic pressures for the two patients would differ by 4.49 mmHg. The answer is B.

A Blood Pressure Measurement Consists of Two Numbers: the Systolic