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 y = ax + b

where a=−0.658 a = -0.658 and b=26.163 b = 26.163 .

Step 2: Substitute the Value of x x

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

y=−0.658×3+26.163 y = -0.658 \times 3 + 26.163

Step 3: Calculate the Predicted Value

Perform the calculation:

y=−0.658×3+26.163=−1.974+26.163=24.189 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:

24.2 \boxed{24.2}

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