Question

rigorous practice schedule, she sometimes has to end a practice session when she begins to experience stiffness. she wonders if stretching more before starting a session will allow her to practice for a longer time.
over the next few days haley varies the number of minutes she stretches before the start of her session, x, and notes the number of minutes she can practice before experiencing stiffness, y.

the least squares regression line of this data set is:

how long of a practice session does this line predict if haley spends 18.02 minutes stretching?
round your answer to the nearest thousandth.

minutes

Explanation:

Step1: Identify the regression line and x value

The regression line is \( y = 4.782x + 148.022 \) and \( x = 18.02 \).

Step2: Substitute x into the regression line

Substitute \( x = 18.02 \) into \( y = 4.782x + 148.022 \):
\( y = 4.782\times18.02 + 148.022 \)
First, calculate \( 4.782\times18.02 \):
\( 4.782\times18.02 = 4.782\times(18 + 0.02)=4.782\times18 + 4.782\times0.02 = 86.076 + 0.09564 = 86.17164 \)
Then, add 148.022:
\( y = 86.17164 + 148.022 = 234.19364 \)

Step3: Round to the nearest thousandth

Rounding 234.19364 to the nearest thousandth gives 234.194.

Answer:

234.194