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A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of sit-ups a person can do (y).

The results of the regression were:
[tex]\[ \hat{y} = ax + b \][/tex]
[tex]\[ a = -0.704 \][/tex]
[tex]\[ b = 29.498 \][/tex]
[tex]\[ r^2 = 0.877969 \][/tex]
[tex]\[ r = -0.937 \][/tex]

Predict the number of sit-ups a person who watches 12.5 hours of TV can do (to one decimal place):
[tex]\[\square\][/tex]



Answer :

GinnyAnswer
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]

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