if the least squares regression line has slope 7 and two x values differ by 2, the predicted difference in the y values is 

In a least squares regression line, the relationship between \( x \) and \( y \) is described by the equation:

\[
y = mx + b
\]

where:
- \( m \) is the slope of the regression line,
- \( b \) is the y-intercept.

Given that the slope is \( 7 \), this means for every 1 unit increase in \( x \), \( y \) increases by \( 7 \) units.

Now, if two \( x \)-values differ by 2, the predicted difference in the corresponding \( y \)-values is calculated by multiplying the slope \( m \) by the difference in \( x \)-values:

\[
\text{Difference in } y = m \times \Delta x = 7 \times 2 = 14
\]

Thus, the predicted difference in the \( y \)-values is \( 14 \).

Would you like more details or have any questions about this?

Here are some related questions:
1. How is the slope of a regression line interpreted in real-world scenarios?
2. What is the meaning of the y-intercept in a regression equation?
3. How can you determine the slope from a set of data points?
4. What are the assumptions behind least squares regression?
5. How does outlier data affect a least squares regression line?

**Tip:** In linear regression, the slope indicates the rate of change in \( y \) for each unit change in \( x \).

If the least squares regression line has slope 7 and two x values differ by 2, the predicted difference in the y values is

Understand how to calculate the predicted difference in y-values when two x-values differ by 2, using a least squares regression line with a slope of 7. This linear regression problem explores key concepts such as slope and linear relationships, suitable for Grades 9-11.

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