Given the regression equation
y hat equals 12.9 plus 6.1 x
and assuming x equals 6 is in the interval of experimental data, find the predicted value when x equals 6.
y hat equals blank. Fill in the blank.

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.

Given the regression equation y hat equals 12.9 plus 6.1 x and assuming x equals 6 is in the interval of experimental data, find the predicted value when x equals 6. y hat equals blank. Fill in the blank.

Find the predicted value using the linear regression equation ŷ = 12.9 + 6.1x when x = 6. This problem demonstrates key concepts in linear regression and algebra. Learn how to substitute values and interpret regression coefficients. Suitable for Grades 9-12.

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