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Read the following description of a data set. A botanist at a university is studying oak trees and the acorns they produce. He collected several acorns from the same tree and measured them.For each acorn, he recorded its volume (in cubic centimeters), $x$ , and its weight (in grams) , $y$ .The least squares regression line of this data set is: $y = 0.485x + 4.938$ $\newline$ Complete the following sentence: $\newline$ For each additional cubic centimeter of acorn volume, the least squares regression line predicts that it would weigh $\_\_$ grams more.

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Interpret regression lines

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Q. Read the following description of a data set. A botanist at a university is studying oak trees and the acorns they produce. He collected several acorns from the same tree and measured them.For each acorn, he recorded its volume (in cubic centimeters),

x

, and its weight (in grams) ,

y

.The least squares regression line of this data set is:

y = 0.485x + 4.938

\newline

Complete the following sentence:

\newline

For each additional cubic centimeter of acorn volume, the least squares regression line predicts that it would weigh

\_\_

grams more.

Regression Line Explanation: The least squares regression line provided is $y = 0.485x + 4.938$ . In this equation, $y$ represents the weight of the acorn in grams, and $x$ represents the volume of the acorn in cubic centimeters. The coefficient of $x$ ( $0.485$ ) indicates the change in weight for each additional cubic centimeter of volume.
Coefficient Interpretation: To find out how much more an acorn would weigh for each additional cubic centimeter of volume, we look at the coefficient of the $x$ variable in the regression equation. This coefficient, $0.485$ , directly tells us the predicted increase in weight (in grams) for each one-unit increase in volume (in cubic centimeters).
Weight Prediction: Therefore, for each additional cubic centimeter of acorn volume, the least squares regression line predicts that the acorn would weigh $0.485$ grams more.

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