Given the regression equation:

$\hat{y} = 12.9 + 6.1x$

To find the predicted value when $x = 6$, substitute $x = 6$ into the equation:

$\hat{y} = 12.9 + 6.1(6)$

$\hat{y} = 12.9 + 36.6$

$\hat{y} = 49.5$

Thus, the predicted value when $x = 6$ is:

$\hat{y} = 49.5$

Would you like any additional details or have any questions?

Here are 5 related questions:

1. How does changing the value of $x$ affect $\hat{y}$ in a linear regression equation?
2. What is the meaning of the coefficients 12.9 and 6.1 in this regression equation?
3. How would the prediction change if $x = 10$?
4. How do you interpret the residual in a regression model?
5. What is the importance of ensuring $x$ is within the interval of experimental data?

Tip: Always check that the value of $x$ used for prediction lies within the range of observed data for better accuracy in regression models.