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 $x$.