To find the value of $y'$ when $x = 6.51$, you can use the equation of the regression line:

$y' = mx + b$

Where:

• $m$ is the slope (2.54),
• $b$ is the y-intercept (17.78),
• $x$ is the value at which we want to calculate $y'$ (6.51).

Substituting the given values into the equation:

$y' = 2.54 \times 6.51 + 17.78$

$y' = 16.54 + 17.78$

$y' = 34.32$

So, the value of $y'$ when $x = 6.51$ is 34.32.

Would you like further explanation on this calculation, or do you have any other questions?

Related Questions:

1. How does changing the slope affect the regression line?
2. What is the significance of the y-intercept in a regression equation?
3. How do you calculate the equation of a regression line from data points?
4. What are residuals in regression analysis, and how do you calculate them?
5. How do you interpret the slope and y-intercept in real-world contexts?

Tip: If you're unsure of the units for slope and intercept, always check your data to make sure they align with each other (for example, if $x$ is in years, $y'$ might be in units like dollars or population).