Question

Use the least squares regression line of this data set to predict a value.
For a science project, Garrett wants to see if a larger body of water has more heat energy than a smaller body of water at the same temperature. He prepared a number of buckets filled with various amounts of water at a fixed temperature and dropped an ice cube of the same size into each one.
Garrett then recorded the volume of water in each bucket (in milliliters), x, and the amount of time it took for each ice cube to melt (in minutes), y.
Volume of water Melting time (in minutes)
468 27.70
733 23.10
756 17.33
854 22.91
888 18.59
992 11.61
The least squares regression line of this data set is:
y=
–
0.026x+40.462
How much time does this line predict it takes for the ice cube to melt in 907 milliliters of water at the fixed temperature?
Round your answer to the nearest thousandth.
minutes

Answer 1

To predict the melting time for 907 milliliters of water using the least squares regression line \( y = -0.026x + 40.462 \), we need to substitute \( x \) with 907 in the equation.

\[
y = -0.026(907) + 40.462
\]

Now, we'll perform the multiplication:

\[
-0.026 \times 907 = -23.582
\]

Next, we add this result to 40.462:

\[
y = -23.582 + 40.462 = 16.880
\]

Therefore, the predicted melting time for the ice cube in 907 milliliters of water is approximately:

\[
\boxed{16.880} \text{ minutes}
\]