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Read the following description of a data set. $\newline$ Antonio runs an apple orchard, and his trees did not produce many apples this season. His friends tell him that adding more fertilizer to the soil may help for next season. Since fertilizer is expensive, Antonio decides to test this theory on some small plots of land with equal area.He varies the kilograms of fertilizer used in each plot, $x$ , and counts the number of apples produced on each, $y$ , at the end of one season.The least squares regression line of this data set is: $y = 1.113x + 331.176$ $\newline$ Complete the following sentence: $\newline$ If one additional kilogram of fertilizer was used in a plot, the least squares regression line predicts an additional ___ apples would be produced on it that season.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

Antonio runs an apple orchard, and his trees did not produce many apples this season. His friends tell him that adding more fertilizer to the soil may help for next season. Since fertilizer is expensive, Antonio decides to test this theory on some small plots of land with equal area.He varies the kilograms of fertilizer used in each plot,

x

, and counts the number of apples produced on each,

y

, at the end of one season.The least squares regression line of this data set is:

y = 1.113x + 331.176

\newline

Complete the following sentence:

\newline

If one additional kilogram of fertilizer was used in a plot, the least squares regression line predicts an additional ___ apples would be produced on it that season.

Identify slope: Identify the slope of the least squares regression line from the given equation $y = 1.113x + 331.176$ . The slope is the coefficient of $x$ , which in this case is $1.113$ .
Interpret slope: Interpret the slope of the regression line. The slope of $1.113$ indicates that for each additional kilogram of fertilizer used, the number of apples produced increases by $1.113$ .
Answer question: Answer the question prompt using the slope. Since the slope is $1.113$ , if one additional kilogram of fertilizer was used in a plot, the least squares regression line predicts an additional $1.113$ apples would be produced on it that season.

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