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use the scatterplot graph above to answer (a)-(c). A) what is the equation of the regression line for all 10 points? round to three decimal places a B) what is the equation of the regression line for the set of 9 points? Round to three decimal places. C) choose the correct description of the results.

To solve the problem, I'll begin by interpreting the points on the scatterplot and answering the given parts accordingly.

### Coordinates of the Points:
The scatterplot has 10 blue points. Let's list their coordinates from the image:

- Point 1: (2, 3)
- Point 2: (5, 6)
- Point 3: (5, 7)
- Point 4: (5, 8)
- Point 5: (6, 6)
- Point 6: (6, 7)
- Point 7: (6, 8)
- Point 8: (7, 6)
- Point 9: (7, 7)
- Point 10: (7, 8)

Now, let’s solve the following:

### A) Equation of the Regression Line for All 10 Points
Using the points listed above, the equation of the regression line is calculated using the formula for a linear regression:

\[ y = mx + b \]

where:
- \( m \) is the slope
- \( b \) is the y-intercept

To find these, we will compute the least squares regression line using all 10 points. I'll calculate it step-by-step using the data extracted.

### B) Equation of the Regression Line for 9 Points
For this part, I need to exclude one point from the calculation. Since the question doesn't specify which point to remove, I will assume the outlier to be (2, 3), as it is quite isolated from the other cluster of points.

### C) Description of the Results
Once I compute both regression lines, I will compare them to provide a description of the results.

Let me now calculate both equations.### A) Regression Line for All 10 Points:
The equation of the regression line for all 10 points is:
\[
y = 0.706x + 2.647
\]
(rounded to three decimal places).

### B) Regression Line for 9 Points:
For the 9 points (excluding (2, 3)), the equation of the regression line is:
\[
y = 0x + 7
\]
This is a horizontal line at \( y = 7 \), as the points form a flat pattern along this y-value.

### C) Description of the Results:
- **For all 10 points**, the regression line has a positive slope, indicating a general upward trend in the data.
- **For the 9 points** (after removing the outlier), the regression line becomes a horizontal line at \( y = 7 \), reflecting that the majority of points are clustered around \( y = 7 \), with no significant slope.

Would you like any further details or clarification on this? 

Here are five related questions:
1. How is the slope of a regression line interpreted in scatterplots?
2. What happens to the regression line when outliers are removed?
3. Why does the regression line change drastically when an outlier is removed?
4. What is the significance of the y-intercept in the regression equation?
5. How would you compute the correlation coefficient for these points?

**Tip:** Outliers can significantly impact the slope and direction of a regression line, especially when they are far from the general cluster of data points.

Use the scatterplot graph to answer (a)-(c): A) What is the equation of the regression line for all 10 points? Round to three decimal places. B) What is the equation of the regression line for the set of 9 points? Round to three decimal places. C) Choose the correct description of the results.

Find the equation of the regression line for a scatterplot of 10 points and compare it with the regression line for 9 points after removing an outlier. Learn how outliers impact the regression line, including step-by-step calculations.

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