Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 m Hg. Use a significance level of 0.05. 101. 168 Right Arm 102 93 80 Left Arm 174 181 144 Click the icon to view the critical values of the Pearson correlation coefficient r 81 145 The regression equation is y=+x. (Round to one decimal place as needed.) .. Given that the systolic blood pressure in the right arm is 85 mm Hg, the best predicted systolic blood pressure in the left arm is ☐ mm Hg. (Round to one decimal place as needed.)
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 m Hg. Use a significance level of 0.05. 101. 168 Right Arm 102 93 80 Left Arm 174 181 144 Click the icon to view the critical values of the Pearson correlation coefficient r 81 145 The regression equation is y=+x. (Round to one decimal place as needed.) .. Given that the systolic blood pressure in the right arm is 85 mm Hg, the best predicted systolic blood pressure in the left arm is ☐ mm Hg. (Round to one decimal place as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 6PPS
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Transcribed Image Text:**Systolic Blood Pressure Regression Analysis**
Below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. We are to find the regression equation, letting the right arm blood pressure serve as the predictor (x) variable. Subsequently, we aim to find the best-predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. We will use a significance level of 0.05.
**Blood Pressure Measurements:**
| Arm | Measurements (mm Hg) |
|-------------|-----------------------|
| **Right Arm** | 102, 101, 93, 80, 81 |
| **Left Arm** | 174, 168, 181, 144, 145 |
**Steps to Follow:**
1. **Find the Regression Equation**:
- Plot the data points with the Right Arm measurements as the x-axis and the Left Arm measurements as the y-axis.
- Determine the regression line that best fits the data, using the least squares method.
- The general form of the regression equation is \( \hat{y} = a + bx \), where:
- \( \hat{y} \) is the predicted value of the dependent variable (Left Arm blood pressure).
- \( a \) is the y-intercept.
- \( b \) is the slope of the regression line.
- Round the values to one decimal place as needed.
2. **Predict the Left Arm Blood Pressure**:
- Given that the systolic blood pressure in the right arm is 85 mm Hg, use the regression equation to predict the systolic blood pressure in the left arm.
- Plug in the value of 85 mm Hg into the regression equation derived in Step 1.
**Graph and Diagram Explanation**:
- The scatter plot graph will display individual data points where the x-axis represents the Right Arm readings and the y-axis represents the Left Arm readings.
- The regression line on this scatter plot helps in visually representing the relationship between the two variables. This line minimizes the sum of the squared differences between the observed values and the line itself.
**Instructions**:
- Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
- Use these critical values to determine the significance of the correlation coefficient.
**Formulas**:
1. The regression equation is \( \hat{
Transcribed Image Text:### Critical Values of the Pearson Correlation Coefficient (r)
The critical values of the Pearson correlation coefficient (r) are used to determine the significance of the correlation between two variables. Below is a table that provides these critical values for different sample sizes (n) and significance levels (α = 0.05 and α = 0.01).
#### Table of Critical Values
| n | α = 0.05 | α = 0.01 |
|----|----------|----------|
| 4 | 0.950 | 0.990 |
| 5 | 0.878 | 0.959 |
| 6 | 0.811 | 0.917 |
| 7 | 0.754 | 0.875 |
| 8 | 0.707 | 0.834 |
| 9 | 0.666 | 0.798 |
| 10 | 0.632 | 0.765 |
| 11 | 0.602 | 0.735 |
| 12 | 0.576 | 0.708 |
| 13 | 0.553 | 0.684 |
| 14 | 0.532 | 0.661 |
| 15 | 0.514 | 0.641 |
| 16 | 0.497 | 0.623 |
| 17 | 0.482 | 0.606 |
| 18 | 0.468 | 0.590 |
| 19 | 0.456 | 0.575 |
| 20 | 0.444 | 0.561 |
| 25 | 0.396 | 0.505 |
| 30 | 0.361 | 0.463 |
| 35 | 0.335 | 0.430 |
| 40 | 0.312 | 0.402 |
| 45 | 0.294 | 0.378 |
| 50 | 0.279 | 0.354 |
| 60 | 0.254 | 0.330 |
| 70 | 0.236
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