https://file.aiquickdraw.com/mathbot/file/1728449880747p0y2h6bz.jpg

using the pairs of values for all 10 points in the picture above, find the equation of the regression line rounded to three decimal places. After removing the point with coordinates (1,2) use the pairs of values for the remaining 9 points and find the equation of the regression line. Compare the results from parts an and b after. 

Let's start by identifying the coordinates of the points from the image:

1. The points in the grid appear to be the following (from visual inspection):
   - (1, 2)
   - (4, 6)
   - (5, 6)
   - (6, 6)
   - (4, 5)
   - (5, 5)
   - (6, 5)
   - (4, 4)
   - (5, 4)
   - (6, 4)

### Step 1: Find the equation of the regression line for all 10 points

We will compute the linear regression equation using the least squares method. The equation of a regression line is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

To calculate this, we will use the formulas:

\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]
\[
b = \frac{\sum y - m(\sum x)}{n}
\]

Where \( n \) is the number of data points, \( \sum xy \) is the sum of the products of each \( x \) and \( y \), and so on.

### Step 2: Remove the point (1, 2) and compute the regression line again

After removing the point (1, 2), we will have 9 data points, and we will repeat the above calculation to find a new equation for the regression line.

### Step 3: Comparison

Once both lines are computed, we'll compare the slopes and intercepts to see how the removal of the outlier (1, 2) affects the regression line.

I will calculate these for you. Let me proceed with these computations now.Here are the results for the regression lines:

### a) Equation of the regression line for all 10 points:
\[
y = 0.529x + 2.265
\]

### b) Equation of the regression line after removing the point (1, 2) (for the remaining 9 points):
\[
y = 0x + 5.0 \quad \text{or simply} \quad y = 5.0
\]

### Comparison:
- The equation with all 10 points has a positive slope of 0.529, indicating an upward trend.
- After removing the point (1, 2), the slope becomes 0, resulting in a horizontal line at \( y = 5 \), showing that without the outlier, the data points align perfectly along \( y = 5 \).

The removal of the outlier significantly changes the regression line, making the trend flatter.

Would you like more details or have any questions? Here are 5 related questions for you to consider:
1. How does the outlier (1, 2) impact the slope and intercept of the regression line?
2. Why does the slope become zero after removing the outlier?
3. How can outliers affect the accuracy of a regression analysis?
4. What are alternative methods to handle outliers in regression?
5. Could there be other outliers affecting the data set?

**Tip:** Outliers can skew results, so it's important to analyze their impact before concluding from a regression analysis.

Using the pairs of values for all 10 points in the picture above, find the equation of the regression line rounded to three decimal places. After removing the point with coordinates (1,2), use the pairs of values for the remaining 9 points and find the equation of the regression line. Compare the results from parts a and b after.

Learn how to calculate the equation of a regression line using 10 points from a coordinate grid and compare the results after removing an outlier point (1, 2). Includes step-by-step analysis, key formulas, and how removing outliers affects the slope and intercept. Suitable for Grade 11-12 students.

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