Use the least squares regression line of this data set to predict a value.

Question

Jen is a professional dancer booked for a major event. Although she has a 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 Jen 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. table: minutes spent stretching: 10.43; 11.52; 14.56; 19.06; 23.68; 25.05. minutes spent practicing: 188; 214; 295; 238; 294; 282. The least squares regression line of this data set is:
y=5.301x+159.689
How long of a practice session does this line predict if Jen spends 12.37 minutes stretching?
Round your answer to the nearest thousandth. _ minutes

Answer 1

To predict the practice session length using the least squares regression line equation \( y = 5.301x + 159.689 \), we will substitute \( x = 12.37 \) (the number of minutes spent stretching) into the equation.

Now, let's calculate it:

\[ y = 5.301(12.37) + 159.689 \]

First, calculate \( 5.301 \times 12.37 \):

\[ 5.301 \times 12.37 \approx 65.50037 \]

Next, add this result to 159.689:

\[ y \approx 65.50037 + 159.689 \approx 225.18937 \]

Rounding to the nearest thousandth, we find:

\[ y \approx 225.189 \]

Therefore, if Jen spends 12.37 minutes stretching, the least squares regression line predicts that she can practice for approximately 225.189 minutes.