Given the regression equation hat y = 15.3 + 7.2x and assuming x = 8 is in the interval of experimental data, find the predicted value when x = 8

To find the predicted value of \( \hat{y} \) when \( x = 8 \) in the regression equation:

\[
\hat{y} = 15.3 + 7.2x
\]

we can substitute \( x = 8 \) into the equation:

\[
\hat{y} = 15.3 + 7.2(8)
\]

Calculating the right side:

1. \( 7.2 \times 8 = 57.6 \)
2. \( 15.3 + 57.6 = 72.9 \)

So, the predicted value when \( x = 8 \) is:

\[
\hat{y} = 72.9
\]

Would you like further details on regression concepts or prediction? 

Here are five follow-up questions that may expand your understanding:

1. How would changes in the coefficient of \( x \) affect the predicted values?
2. What does the intercept (15.3) represent in this regression context?
3. How can we interpret the slope (7.2) of this regression equation?
4. What methods can assess the accuracy of this regression prediction?
5. How would you calculate the residual if you had an observed \( y \) value for \( x = 8 \)?

**Tip:** In a regression equation, the slope indicates the expected change in \( y \) for a one-unit increase in \( x \).

Learn how to find the predicted value when x = 8 using the linear regression equation y = 15.3 + 7.2x. This guide includes a step-by-step solution to calculate predictions within a regression model, focusing on key concepts in algebra and regression for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation