**Why do we square the residuals when using the least-squares line method to find the line of best fit?**

A.)

It amplifies the effect of having negative and positive residuals.

B.)

Squaring the residuals makes it easier to identify smaller residuals.

C.)

We don't square the residuals when using the least-squares method.

D.)

It cancels out the effect of having negative and positive residuals.

The correct answer is:

**D.) It cancels out the effect of having negative and positive residuals.**

Explanation: 

When calculating the line of best fit using the least-squares method, we square the residuals to eliminate the issue of positive and negative residuals canceling each other out. Residuals represent the difference between the observed data points and the predicted values from the line. Without squaring, the negative residuals would offset the positive ones, leading to an inaccurate measure of the total error. Squaring ensures that all residuals contribute positively to the total error, and the line minimizes this sum of squared errors.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the definition of residuals in regression analysis?
2. How is the least-squares line method derived mathematically?
3. What are the consequences of not squaring residuals in least squares regression?
4. Can the least-squares method handle outliers effectively?
5. What other methods exist for finding the line of best fit besides least squares?

**Tip:** Squaring emphasizes larger errors more than smaller ones, making least squares sensitive to outliers in the data.

Why do we square the residuals when using the least-squares line method to find the line of best fit?

Discover why squaring residuals is essential in the least-squares method to find the line of best fit. Learn how this process cancels out the effect of negative and positive residuals to accurately measure error. Ideal for students in Grades 10-12 studying regression analysis.

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