To determine the predicted value of $y$ when $x = 2$ using the provided linear regression equation, we can substitute $x = 2$ into the regression equation:

$y = 5.22x - 13.11$

Substituting $x = 2$:

$y = 5.22(2) - 13.11$

$y = 10.44 - 13.11$

$y = -2.67$

So, the predicted value of $y$ when $x = 2$ is -2.67.

Would you like more details on this calculation or have any other questions?

Here are 5 related questions you might find interesting:

1. How is the coefficient of determination (R-squared) interpreted in this context?
2. What does the T-value in the regression output signify?
3. How does the adjusted R-squared differ from the R-squared value?
4. What is the significance of the standard error of the coefficients?
5. How would the prediction change if the constant term was different?

Tip: The closer the R-squared value is to 100%, the better the model fits the data.