← 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 95 mm Hg. Use a significance level of 0.05. Right Arm 101 100 93 79 Left Arm 176 171 143 145 Click the icon to view the critical values of the Pearson correlation coefficient r • The regression equation is y=+x. X. (Round to one decimal place as needed.) 80 144 ... Given that the systolic blood pressure in the right arm is 95 mm Hg, the best predicted systolic blood pressure in the left arm is (Round to one decimal place as needed.) mm Hg.

MATLAB: An Introduction with Applications
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### Data Table: Critical Values of the Pearson Correlation Coefficient (r)

This table provides the critical values of the Pearson correlation coefficient (r) for different sample sizes (n) at significance levels of α = 0.05 and α = 0.01. The critical values are used in hypothesis testing to determine whether to reject the null hypothesis (H₀) that there is no correlation (ρ = 0) against the alternative hypothesis (H₁) that there is a non-zero correlation (ρ ≠ 0).

#### Critical Values Table:

| 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
Transcribed Image Text:### Data Table: Critical Values of the Pearson Correlation Coefficient (r) This table provides the critical values of the Pearson correlation coefficient (r) for different sample sizes (n) at significance levels of α = 0.05 and α = 0.01. The critical values are used in hypothesis testing to determine whether to reject the null hypothesis (H₀) that there is no correlation (ρ = 0) against the alternative hypothesis (H₁) that there is a non-zero correlation (ρ ≠ 0). #### Critical Values Table: | 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
### Educational Exercise: Predicting Systolic Blood Pressure

#### Systolic Blood Pressure Data
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. The goal is to find the regression equation, letting the right arm blood pressure be the predictor (x) variable. We will use these data to predict the systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 95 mm Hg. The significance level is 0.05.

|            | Blood Pressure (mm Hg) |
|------------|-------------------------|
| **Right Arm** | 101 | 100 | 93  | 79  | 80  |
| **Left Arm**  | 176 | 171 | 143 | 145 | 144 |

#### Tasks:
1. **Regression Equation:** Derive the regression equation in the form of \( \hat{y} = b_0 + b_1x \).
   - Round the coefficients to one decimal place as needed.

2. **Prediction:** Given that the systolic blood pressure in the right arm is 95 mm Hg, use the regression equation to find the best-predicted systolic blood pressure in the left arm.
   - Round the result to one decimal place as needed.

#### Input Fields:
- The regression equation is \( \hat{y} = \_\_\_ + \_\_\_ x \).
  (Round to one decimal place as needed.)
  
- Given that the systolic blood pressure in the right arm is 95 mm Hg, the best predicted systolic blood pressure in the left arm is \_\_\_\_ mm Hg. 
  (Round to one decimal place as needed.)

#### Additional Resources:
- Click the icon provided in the original interface to view the critical values of the Pearson correlation coefficient \( r \).

This exercise helps in understanding the application of linear regression analysis in predicting one variable based on the observed values of another variable. It is essential in fields such as statistics, healthcare, and data science.
Transcribed Image Text:### Educational Exercise: Predicting Systolic Blood Pressure #### Systolic Blood Pressure Data Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. The goal is to find the regression equation, letting the right arm blood pressure be the predictor (x) variable. We will use these data to predict the systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 95 mm Hg. The significance level is 0.05. | | Blood Pressure (mm Hg) | |------------|-------------------------| | **Right Arm** | 101 | 100 | 93 | 79 | 80 | | **Left Arm** | 176 | 171 | 143 | 145 | 144 | #### Tasks: 1. **Regression Equation:** Derive the regression equation in the form of \( \hat{y} = b_0 + b_1x \). - Round the coefficients to one decimal place as needed. 2. **Prediction:** Given that the systolic blood pressure in the right arm is 95 mm Hg, use the regression equation to find the best-predicted systolic blood pressure in the left arm. - Round the result to one decimal place as needed. #### Input Fields: - The regression equation is \( \hat{y} = \_\_\_ + \_\_\_ x \). (Round to one decimal place as needed.) - Given that the systolic blood pressure in the right arm is 95 mm Hg, the best predicted systolic blood pressure in the left arm is \_\_\_\_ mm Hg. (Round to one decimal place as needed.) #### Additional Resources: - Click the icon provided in the original interface to view the critical values of the Pearson correlation coefficient \( r \). This exercise helps in understanding the application of linear regression analysis in predicting one variable based on the observed values of another variable. It is essential in fields such as statistics, healthcare, and data science.
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