Questions: 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: y=ax+b a=-0.658 b=26.163 r^2=0.964324 r=-0.982 Use this to predict the number of situps a person who watches 3 hours of TV can do (to one decimal place)

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: y=ax+b a=-0.658 b=26.163 r^2=0.964324 r=-0.982 Use this to predict the number of situps a person who watches 3 hours of TV can do (to one decimal place)
Transcript text: A regression was run to determine if there is a relationship between hours of TV watched per day $(\mathrm{x})$ and number of situps a person can do (y). The results of the regression were: \[ \begin{array}{l} y=a x+b \\ a==-0.658 \\ b=26.163 \\ r^{2}=0.964324 \\ r=-0.982 \end{array} \] Use this to predict the number of situps a person who watches 3 hours of TV can do (to one decimal place) $\square$
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Solution

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Solution Steps

Step 1: Understand the Regression Equation

The regression equation given is:

\[ y = ax + b \]

where \( a = -0.658 \) and \( b = 26.163 \).

Step 2: Substitute the Value of \( x \)

We need to predict the number of situps (\( y \)) for a person who watches 3 hours of TV per day. Substitute \( x = 3 \) into the regression equation:

\[ y = -0.658 \times 3 + 26.163 \]

Step 3: Calculate the Predicted Value

Perform the calculation:

\[ y = -0.658 \times 3 + 26.163 = -1.974 + 26.163 = 24.189 \]

Final Answer

The predicted number of situps a person who watches 3 hours of TV can do is:

\[ \boxed{24.2} \]

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