For a science project, Michael 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.
Michael 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.
The least squares regression line of this data set is:
y= –0.026x + 44.506
How much time does this line predict it takes for the ice cube to melt in 414 milliliters of water at the fixed temperature?
Round your answer to the nearest thousandth.
______ minutes
To find out how much time the regression line predicts it takes for the ice cube to melt in 414 milliliters of water, we plug 414 into the equation for x:
y = -0.026(414) + 44.506
y = -10.764 + 44.506
y ≈ 33.742
Therefore, the regression line predicts it takes approximately 33.742 minutes for the ice cube to melt in 414 milliliters of water at the fixed temperature.