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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: $y = 1.697x - 8.247$ $\newline$ 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 = 1.697x - 8.247

\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.

Regression Line Equation: The least squares regression line is given by the equation $y = 1.697x - 8.247$ . In this equation, $y$ represents the number of tablets taken, and $x$ represents the number of headaches.
Coefficient of x: The coefficient of x in the equation, which is $1.697$ , represents the slope of the line. This slope tells us how much $y$ is expected to increase for each additional unit increase in $x$ . In the context of this problem, it means that for each additional headache, the number of tablets taken is expected to increase by $1.697$ .
Interpretation: Therefore, for each additional headache someone had, the least squares regression line predicts that he or she would have taken $1.697$ additional tablets.

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