DO THE CALCULATION AND DESPRBE THE SFATTER PLOT FOR MRSAN WHICH UN THE HRIZENTAL AND WTCH IN THE VERTUAL . AND I HAVE QST IS THIS TABKE I GAVE U SWAPPED? X AND Y ??

### Scatter Plot Description
The scatter plot visualizes the relationship between the **Dosage (X in ml)** on the horizontal axis and **Time of Hospitalization (Y in months)** on the vertical axis. The data points are scattered without a strong visible trend, indicating a weak or negligible correlation between the dosage and the time spent in the hospital.

### Key Calculations
1. **Pearson Correlation Coefficient**:
   - The correlation coefficient \( r \) is approximately **0.198**, suggesting a very weak positive correlation between dosage and hospitalization time. This weak correlation implies that increasing or decreasing the dosage has minimal effect on the time a patient stays in the hospital.

2. **Regression Line**:
   - The equation of the regression line \( Y \) on \( X \) is:
     \[
     Y = 0.228X + 2.83
     \]
   - This line represents the best-fit line through the scatter plot points, but given the weak correlation, it should be interpreted with caution.

3. **Standard Error**:
   - The standard error of the slope is **0.157**, indicating the variability of the slope estimate.

4. **Regression Line Values**:
   - For the given dosage values in the table, the corresponding predicted hospitalization times (from the regression line) are:
     - For \( X = 1.5 \) ml: \( Y \approx 3.17 \) months
     - For \( X = 3.0 \) ml: \( Y \approx 3.52 \) months
     - For \( X = 4.5 \) ml: \( Y \approx 3.86 \) months
     - For \( X = 6.0 \) ml: \( Y \approx 4.20 \) months
     - For \( X = 6.5 \) ml: \( Y \approx 4.31 \) months

### Conclusion and Answer to Your Question
- **Is the table swapped?**: No, the table is correctly presented with **Dosage (X)** on the horizontal axis and **Time of Hospitalization (Y)** on the vertical axis.
- The weak correlation suggests that dosage might not be a strong predictor of hospitalization time. 

If you need further details or have additional questions, feel free to ask!

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**5 Relative Questions:**

1. How does the weak correlation affect the interpretation of the regression model?
2. What other variables could be investigated to understand the factors affecting hospitalization time?
3. What would be the impact on the results if the dosage was standardized?
4. How would the interpretation change if the correlation was negative?
5. Can we consider the dosage as an independent factor in this medical study, given the weak correlation?

**Tip:** Always be cautious when interpreting regression models with low correlation coefficients, as the predictive power may be limited.

Explore the relationship between dosage and time of hospitalization through a scatter plot analysis. Learn about the weak correlation observed, Pearson correlation coefficient, regression line equation, and the impact of dosage on hospitalization time. Suitable for advanced high school and undergraduate students studying statistics and regression analysis.

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