Calculate the least squares line.           x: 1,,1,2,2,10    y:1,3,1,3,10

Given the data points:

- \( x: 1, 1, 2, 2, 10 \)
- \( y: 1, 3, 1, 3, 10 \)

We will calculate the slope \( m \) and y-intercept \( b \) using the same formulas as before:

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

\[
b = \frac{\sum{y} - m\sum{x}}{n}
\]

Let's calculate these values.The equation of the least squares line for the given data points is:

\[
y = 0.925x + 0.639
\]

This line best fits the provided data using the least squares method.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would removing the outlier (10, 10) affect the least squares line?
2. Can we interpret the slope and intercept of this line in the context of these data points?
3. How does the least squares line compare to a line fitted by another method, like median fitting?
4. What is the coefficient of determination \( R^2 \) for this line?
5. How does the presence of repeated \( x \) values affect the least squares calculation?

**Tip:** When dealing with potential outliers in data, it's important to consider their influence on the least squares line, as they can significantly skew the results.

Learn how to calculate the least squares line for given data points x = [1, 1, 2, 2, 10] and y = [1, 3, 1, 3, 10]. This problem involves using the least squares method to determine the line of best fit, including formulas for slope and y-intercept calculations.

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