To predict the number of situps a person can do based on the number of hours of TV they watch per day, we will use the regression equation provided:
[tex]\[
\hat{y} = a x + b
\][/tex]
where:
- [tex]\(\hat{y}\)[/tex] is the predicted number of situps,
- [tex]\(x\)[/tex] is the number of hours of TV watched per day,
- [tex]\(a\)[/tex] is the slope of the regression line,
- [tex]\(b\)[/tex] is the y-intercept of the regression line.
From the regression results given:
- [tex]\(a = -0.704\)[/tex]
- [tex]\(b = 29.498\)[/tex]
- [tex]\(x = 12.5\)[/tex] hours of TV per day
We substitute these values into the regression equation to predict the number of situps:
[tex]\[
\hat{y} = (-0.704)(12.5) + 29.498
\][/tex]
First, we calculate the product of [tex]\(-0.704\)[/tex] and [tex]\(12.5\)[/tex]:
[tex]\[
-0.704 \times 12.5 = -8.8
\][/tex]
Next, we add this result to the y-intercept [tex]\(b\)[/tex]:
[tex]\[
-8.8 + 29.498 = 20.698
\][/tex]
Therefore, the predicted number of situps a person who watches 12.5 hours of TV per day can do is:
[tex]\[
\boxed{20.7}
\][/tex]
