Given the regression equation
y hat equals 8.4 plus 5.3 x
and assuming x equals 12 is in the interval of experimental data, find the predicted value when x equals 12.
y hat equals blank. Fill in the blank.


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.

Given the regression equation y hat equals 8.4 plus 5.3 x and assuming x equals 12 is in the interval of experimental data, find the predicted value when x equals 12. y hat equals blank. Fill in the blank.

Learn how to find the predicted value of ŷ for the regression equation ŷ = 8.4 + 5.3x when x = 12. This example explains the basics of linear regression and provides a clear step-by-step solution, suitable for students in Grades 9-12.

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