Given the regression equation:

$\hat{y} = 8.4 + 5.3x$

and $x = 12$, substitute 12 for $x$ in the equation:

$\hat{y} = 8.4 + 5.3(12)$

Now, calculate:

$\hat{y} = 8.4 + 63.6 = 72$

Thus, the predicted value when $x = 12$ is:

$\hat{y} = 72$

Would you like more details or further clarification?

Related Questions:

1. How does changing the value of $x$ affect the predicted $\hat{y}$?
2. What is the meaning of the slope $5.3$ in this regression equation?
3. How do we interpret the intercept $8.4$ in this equation?
4. What if $x = 15$, how would the predicted value change?
5. What is the significance of ensuring $x = 12$ is within the interval of experimental data?

Tip: Always check that your data points fall within the experimental range of values before making predictions in regression models.