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Read the following description of a data set. $\newline$ For a science project, Maya wants to see if a larger body of water has more heat energy than a smaller body of water at the same temperature. She 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.Maya 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: $y = -0.008x + 27.243$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts that if the volume of water increases by one milliliter, the time it takes for the ice cube to melt will drop by $\_\_$ minutes.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

For a science project, Maya wants to see if a larger body of water has more heat energy than a smaller body of water at the same temperature. She 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.Maya 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 = -0.008x + 27.243

\newline

Complete the following sentence:

\newline

The least squares regression line predicts that if the volume of water increases by one milliliter, the time it takes for the ice cube to melt will drop by

\_\_

minutes.

Understand Coefficients Meaning: To solve this problem, we need to understand the meaning of the coefficients in the least squares regression line equation. The equation given is $y = -0.008x + 27.243$ , where $y$ represents the time it takes for the ice cube to melt, and $x$ represents the volume of water in milliliters.
Interpret Coefficient of $x$ : The coefficient of $x$ in the equation is $-0.008$ . This coefficient tells us how much the dependent variable ( $y$ , time to melt) changes for each one-unit increase in the independent variable ( $x$ , volume of water). Since the coefficient is negative, it indicates that the time decreases as the volume increases.
Calculate Time Change: To find out how much the time changes when the volume increases by $1$ milliliter, we can simply look at the coefficient of $x$ , which is $-0.008$ . This means that for every additional milliliter of water, the time it takes for the ice cube to melt decreases by $0.008$ minutes.

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