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Pictured above are the critical values of the Pearson correlation coefficient r. The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. If one of these people has a systolic blood pressure of 137 mm Hg, what is the best predicted diastolic blood pressure? The data for systolic blood pressure is as follows in respective order : 122, 134, 143, 140, 135, 113, 110, 145. The data for diastolic blood pressure in respective order is as follows : 62,71, 80,80, 100,59, 82, 105. find the regression equation and round to two decimal places as needed. 

To solve this, we need to calculate the linear regression equation in the form \( y = mx + b \), where:

- \( y \) represents the diastolic blood pressure (dependent variable).
- \( x \) represents the systolic blood pressure (independent variable).
- \( m \) is the slope of the regression line.
- \( b \) is the y-intercept.

### Step 1: Organize the data

The systolic (x) and diastolic (y) blood pressures are given as:

\[
x = \{122, 134, 143, 140, 135, 113, 110, 145\}
\]
\[
y = \{62, 71, 80, 80, 100, 59, 82, 105\}
\]

### Step 2: Calculate the necessary values

We will use the following formulas for the slope \( m \) and the intercept \( b \):

\[
m = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}
\]
\[
b = \frac{\sum y - m \sum x}{n}
\]

Where:
- \( n \) is the number of data points (in this case, \( n = 8 \)).
- \( \sum x \) is the sum of the x-values.
- \( \sum y \) is the sum of the y-values.
- \( \sum xy \) is the sum of the products of corresponding x and y values.
- \( \sum x^2 \) is the sum of the squares of the x-values.

Let me calculate these values now.The regression equation is:

\[
y = 0.70x - 11.20
\]

### Step 3: Use the regression equation to predict the diastolic blood pressure for a systolic blood pressure of 137 mm Hg.

We substitute \( x = 137 \) into the equation:

\[
y = 0.70(137) - 11.20
\]

Let me calculate that now.The best predicted diastolic blood pressure for a systolic blood pressure of 137 mm Hg is approximately **84.59 mm Hg**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the Pearson correlation coefficient, and how is it related to the regression equation?
2. How would the prediction change if we had more data points for systolic and diastolic blood pressures?
3. What assumptions are we making when using linear regression to predict diastolic blood pressure?
4. How can you assess the goodness of fit for this regression model?
5. What is the significance of the slope and intercept in a regression equation?

**Tip:** In regression, always check the Pearson correlation coefficient to determine the strength of the linear relationship before interpreting the regression equation!

Pictured above are the critical values of the Pearson correlation coefficient r. The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. If one of these people has a systolic blood pressure of 137 mm Hg, what is the best predicted diastolic blood pressure? The data for systolic blood pressure is as follows in respective order: 122, 134, 143, 140, 135, 113, 110, 145. The data for diastolic blood pressure in respective order is as follows: 62,71, 80,80, 100,59, 82, 105.

Learn how to find the regression equation for systolic and diastolic blood pressure. The systolic blood pressure readings are 122, 134, 143, 140, 135, 113, 110, 145, and the diastolic readings are 62, 71, 80, 80, 100, 59, 82, 105. The regression equation can predict the diastolic pressure when the systolic pressure is given.

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