Question

Use the least squares regression line of this data set to predict a value.
Coach Chapman is responsible for recruiting male athletes to join the European Masters track and field team. To improve her recruitment strategies, she wants to investigate the connection between an athlete's height and 3000-meter run time.
Coach Chapman has recorded the heights of the men on the track and field team (in centimeters), x, and their best 3000-meter times (in minutes), y.
Height 3000-meter time
157 8.58
162 8.47
164 7.98
175 8.45
183 7.55
The least squares regression line of this data set is:
y=
–
0.029x+13.072
How quickly does this line predict a man who is 180 centimeters tall would run the 3000-meters?
Round your answer to the nearest thousandth.
minutes

Answer 1

To predict the 3000-meter run time for a man who is 180 centimeters tall using the least squares regression line \( y = -0.029x + 13.072 \), we can substitute \( x = 180 \) into the equation.

Starting with the equation:

\[
y = -0.029(180) + 13.072
\]

Calculating \( -0.029(180) \):

\[
-0.029 \times 180 = -5.22
\]

Now, substitute this value back into the equation:

\[
y = -5.22 + 13.072
\]
\[
y = 7.852
\]

So, the predicted 3000-meter run time for a man who is 180 centimeters tall is approximately **7.852 minutes**.

Rounded to the nearest thousandth, the answer is:

**7.852 minutes**.