y=ax+b
a=-1.391
b=25.411
r2=0.528529
r=-0.727



Use this to predict the number of situps a person who watches 10.5 hours of TV can do (to one decimal place)


To predict the number of sit-ups a person who watches 10.5 hours of TV can do, we can use the linear equation provided:

\[
y = ax + b
\]

where:
- \( a = -1.391 \)
- \( b = 25.411 \)
- \( x \) represents the number of hours of TV watched
- \( y \) represents the predicted number of sit-ups

We need to find \( y \) when \( x = 10.5 \):

\[
y = -1.391(10.5) + 25.411
\]

Let's calculate this:

\[
y = -1.391 \times 10.5 + 25.411
\]
\[
y = -14.6055 + 25.411
\]
\[
y = 10.8055
\]

Rounded to one decimal place, the predicted number of sit-ups is **10.8**.

Would you like more details or have any questions?

Here are five related questions:
1. How does the \( r^2 \) value influence the accuracy of this prediction?
2. What would be the predicted number of sit-ups if a person watches 5 hours of TV?
3. How would the prediction change if the slope \( a \) were steeper, say \( -2.5 \)?
4. Can you interpret the meaning of the negative \( r \) value in this context?
5. If the number of hours of TV watched increased to 15 hours, what would the predicted number of sit-ups be?

**Tip:** The \( r^2 \) value, also known as the coefficient of determination, gives insight into how well the independent variable explains the variability of the dependent variable. A value closer to 1 indicates a better fit.

Learn how to predict the number of sit-ups a person can do based on hours of TV watched using linear regression. This problem involves calculating predictions using the linear equation y = ax + b with given coefficients. Suitable for students in Grades 9-12.

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