Question

The data below shows the systolic and diastolic blood pressures of 10 patients, and we know the correlation exists. Find the linear regression equation, using the systolic blood pressure as the independent variable, and find the best predicted diastolic blood pressure for a patient with a systolic blood pressure reading of 140.

Systolic Diastolic
116 82
124 88
112 72
144 95
138 96
112 76
145 88
124 76
130 90
129 94

Answer 1

The linear regression is diastolic = 51.97 + 0.5114 * systolic.

The best predicted diastolic blood pressure for a systolic blood pressure of 140 is 118.33.

Step-by-step explanation:

To find the linear regression equation, we will use the method of least squares.

We will calculate the slope and intercept of the regression line using the formula:

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

intercept = (Σy - slopeΣx) / n

Plugging in the given data, we find the equation of the regression line:

diastolic = 51.97 + 0.5114 * systolic

To find the predicted diastolic blood pressure for a systolic blood pressure reading of 140, we substitute the value into the equation:

diastolic = 51.97 + 0.5114 * 140

= 118.33