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The image shows a scatter plot of data points that represent the relationship between the "amount of medication" (in mg) and "patient systolic blood pressure" (in mm Hg). A linear regression line has been fitted to the data, showing the trend of how blood pressure decreases as the amount of medication increases.

The given regression equation for this plot is partially completed:

\[
\hat{Y} = \text{Ex: 40} + \text{Ex: 0.43} \cdot X
\]

From the notation, it appears the unknown values should represent the intercept and slope of the regression line. Let’s address how to interpret this.

- **\( \hat{Y} \)** represents the predicted systolic blood pressure.
- **\( X \)** represents the amount of medication in mg.
- The intercept (missing value for Ex: 40) is likely around 140 mm Hg, indicating the blood pressure when no medication is given.
- The slope (Ex: 0.43) represents the rate of decrease in blood pressure per mg of medication. However, based on the slope, this value is negative because blood pressure decreases as the medication increases.

Therefore, the corrected regression equation might be:

\[
\hat{Y} = 140 - 0.43 \cdot X
\]

Here’s a breakdown of the interpretation:
- **140** is the estimated systolic blood pressure when no medication is taken.
- **-0.43** means that for each additional milligram of medication, the systolic blood pressure decreases by approximately 0.43 mm Hg.

Would you like more details or explanations on this? 

Here are 5 related questions to further explore this topic:
1. How is the slope of a regression line interpreted in medical studies like this one?
2. What are the assumptions behind using a linear regression model for this type of data?
3. How could we calculate the predicted blood pressure for a given amount of medication?
4. How do you determine if the regression line is a good fit for the data?
5. What is the significance of the intercept value in the context of medication dosage?

**Tip:** Always check the sign of the slope to understand the direction of the relationship between variables in regression.

A medical researcher wants to determine how a new medication affects blood pressure. The scatter plot shows the relationship between the amount of medication (in mg) and patient systolic blood pressure (in mm Hg). The regression equation is partially given as: Ŷ = Ex: 40 + Ex: 0.43 X.

Explore the linear regression model analyzing the effect of medication dosage on patient systolic blood pressure. This example includes a scatter plot and regression line, predicting how blood pressure decreases as the medication increases. Suitable for Grades 10-12, this problem explains key concepts in linear regression, including slope interpretation and the regression equation.

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