A regression was run to determine if there is a relationship between hours of TV watched per day $$ (x) $$ and number of situps a person can do $$ (y) $$. The results of the regression were: $$ \begin{array}{l}y=a x+b \ a=-1.185 \ b=21.393 \ r^{2}=0.3969 \ r=-0.63\end{array} $$ Use this to predict the number of situps a person who watches 3 hours of TV can do (to one decimal place).

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UpStudy AI · Accepted Answer

To predict the number of sit-ups a person can do based on the hours of TV watched, we will use the regression equation provided:

$$
y = ax + b
$$

where:
- $$ a = -1.185 $$
- $$ b = 21.393 $$
- $$ x = 3 $$ (the number of hours of TV watched)

Now, we will substitute the values of $$ a $$, $$ b $$, and $$ x $$ into the equation:

$$
y = -1.185(3) + 21.393
$$

Let's calculate this step by step:

1. Calculate $$ -1.185 \times 3 $$:
   $$
   -1.185 \times 3 = -3.555
   $$

2. Now, add $$ 21.393 $$ to the result:
   $$
   y = -3.555 + 21.393
   $$

3. Perform the addition:
   $$
   y = 17.838
   $$

Finally, rounding to one decimal place, we get:

$$
y \approx 17.8
$$

Thus, the predicted number of sit-ups a person who watches 3 hours of TV can do is approximately **17.8**.
A person who watches 3 hours of TV can do approximately 17.8 sit-ups.

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