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 (), for a sample of adults. The following table presents the results.

Question

systolic
123
119
118
130
116
133
112
107
110
108
diastolic
77
69
88
76
70
91
75
71
74
69

The regression line equation is 13.4677+0.5317x

If the systolic pressures of two patients differ by 9 millimeters, by how much would you predict their diastolic pressures to differ? Round the answer to three decimal places.

Answer 1

To find out how much the diastolic pressures of two patients would differ based on the difference in their systolic pressures, we can use the slope of the regression line.

The regression line equation is given as:

\[ \text{Diastolic pressure} = 13.4677 + 0.5317 \times (\text{Systolic pressure}) \]

The slope of 0.5317 indicates the change in diastolic pressure for each 1 millimeter change in systolic pressure.

If the systolic pressures of two patients differ by 9 millimeters, we can calculate the predicted difference in diastolic pressures as follows:

\[ \text{Predicted difference in diastolic pressure} = \text{slope} \times \text{difference in systolic pressure} \]

Substituting the values:

\[ \text{Predicted difference in diastolic pressure} = 0.5317 \times 9 \]

Now, performing the calculation:

\[ \text{Predicted difference in diastolic pressure} = 0.5317 \times 9 = 4.7853 \]

Rounding to three decimal places gives:

\[ \text{Predicted difference in diastolic pressure} \approx 4.785 \]

Thus, if the systolic pressures of two patients differ by 9 millimeters, we would predict their diastolic pressures to differ by approximately 4.785 millimeters.

Answer 2

Predict the diastolic pressure for a patient whose systolic pressure is 127 millimeters. Round the answer to one decimal place.

Answer 3

To predict the diastolic pressure for a patient with a systolic pressure of 127 millimeters using the given regression line equation:

\[ \text{Diastolic pressure} = 13.4677 + 0.5317 \times (\text{Systolic pressure}) \]

We can substitute the systolic pressure of 127 into the equation:

\[ \text{Diastolic pressure} = 13.4677 + 0.5317 \times 127 \]

Now, calculate \(0.5317 \times 127\):

\[ 0.5317 \times 127 = 67.1969 \]

Now, add this value to 13.4677:

\[ \text{Diastolic pressure} = 13.4677 + 67.1969 = 80.6646 \]

Rounding this result to one decimal place gives:

\[ \text{Diastolic pressure} \approx 80.7 \]

Thus, the predicted diastolic pressure for a patient whose systolic pressure is 127 millimeters is approximately 80.7 mmHg.