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Read the following description of a data set. $\newline$ A pharmaceutical company is testing a new headache medication. Researchers at the company conducted an observational study using volunteer participants. All participants were given a supply of tablets of the new medication.The participants then recorded how many headaches they had had for a week, $x$ , and how many tablets they had taken, $y$ .The least squares regression line of this data set is: $y = 1.518x - 0.226$ $\newline$ Complete the following sentence: $\newline$ For each additional headache someone had had, the least squares regression line predicts that he or she would have taken ___ additional tablets.

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Interpret regression lines

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Q. Read the following description of a data set.

\newline

A pharmaceutical company is testing a new headache medication. Researchers at the company conducted an observational study using volunteer participants. All participants were given a supply of tablets of the new medication.The participants then recorded how many headaches they had had for a week,

x

, and how many tablets they had taken,

y

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

y = 1.518x - 0.226

\newline

Complete the following sentence:

\newline

For each additional headache someone had had, the least squares regression line predicts that he or she would have taken ___ additional tablets.

Identify Slope: Identify the slope of the least squares regression line. The equation given is $y = 1.518x - 0.226$ . The slope of the least squares regression line is the coefficient of $x$ , which is $1.518$ . This slope indicates the change in the number of tablets taken ( $y$ ) for each additional headache ( $x$ ).
Interpret Slope: Interpret the slope. $\newline$ Since the slope is $1.518$ , this means that for each additional headache a person has, the least squares regression line predicts that they would take $1.518$ additional tablets.

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