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A fitness coach wants to know if stretching before running helps reduce how long runners feel sore afterward. She conducted a study where participants recorded how many minutes they stretched before their run and how many hours they felt sore afterward. Here is the data she collected: Use the Desmos Graphing Calculator (right-click and open in new tab/window) to calculate the following: r = -0.6721 y = -0.415 x + 11.947 If someone was to stretch for 5 minutes, what would the regression line predict for the duration of soreness? 8.152

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To predict the duration of soreness based on the amount of stretching using the regression line, we can use the regression equation given:

\[ y = -0.415x + 11.947 \]

Where:

  • \( y \) is the predicted duration of soreness (in hours),
  • \( x \) is the number of minutes stretched.

If someone stretches for 5 minutes, we can substitute \( x = 5 \) into the equation:

\[ y = -0.415(5) + 11.947 \]

Calculating this step-by-step:

  1. Multiply -0.415 by 5: \[ -0.415 \times 5 = -2.075 \]

  2. Add this result to 11.947: \[ y = -2.075 + 11.947 = 9.872 \]

So, if someone stretches for 5 minutes, the regression line predicts that they will feel sore for approximately 9.872 hours afterward.