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Read the following description of a data set. $\newline$ Grape growers in France think they will have a massive crop this year and want to know how this will influence demand for grape juice.They compared how many grapes were produced (in millions of metric tons), $x$ , and the amount of French grape juice that was sold in previous years (in billions of liters), $y$ .The least squares regression line of this data set is: $y = 0.143x + 5.363$ $\newline$ Complete the following sentence: $\newline$ The least squares regression line predicts the amount of French grape juice sold would increase by ___ billion liters if the amount of grapes produced increased by one million metric tons.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Grape growers in France think they will have a massive crop this year and want to know how this will influence demand for grape juice.They compared how many grapes were produced (in millions of metric tons),

x

, and the amount of French grape juice that was sold in previous years (in billions of liters),

y

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

y = 0.143x + 5.363

\newline

Complete the following sentence:

\newline

The least squares regression line predicts the amount of French grape juice sold would increase by ___ billion liters if the amount of grapes produced increased by one million metric tons.

Analyze Equation: Analyze the given regression equation $y = 0.143x + 5.363$ . Here, the slope is $0.143$ , which represents the change in $y$ (amount of French grape juice sold in billions of liters) for each unit increase in $x$ (amount of grapes produced in millions of metric tons).
Calculate Increase Rate: To find out how much the sale of French grape juice increases per one million metric tons increase in grape production, look at the slope of the regression line, which is $0.143$ . This means for every one million metric tons increase in grape production, the sale of grape juice increases by $0.143$ billion liters.

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