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Read the following description of a data set. Researchers at a pharmaceutical company are testing a new drug that regulates blood sugar. In one test, subjects were prescribed a random and safe dose of the drug. Once the drugs were administered, the researchers measured each subject's blood sugar levels before and after a meal.For each subject, the company recorded the given dose (in milligrams), $x$ , and the rise in blood sugar (in milligrams per deciliter), $y$ .The least squares regression line of this data set is: $y = -0.004x + 28.109$ $\newline$ Complete the following sentence: $\newline$ If the dose increased by $1$ milligram, the least squares regression line predicts that a subjects' blood sugar level will rise $\_\_$ milligrams per deciliter less.

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Interpret regression lines

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Q. Read the following description of a data set. Researchers at a pharmaceutical company are testing a new drug that regulates blood sugar. In one test, subjects were prescribed a random and safe dose of the drug. Once the drugs were administered, the researchers measured each subject's blood sugar levels before and after a meal.For each subject, the company recorded the given dose (in milligrams),

x

, and the rise in blood sugar (in milligrams per deciliter),

y

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

y = -0.004x + 28.109

\newline

Complete the following sentence:

\newline

If the dose increased by

1

milligram, the least squares regression line predicts that a subjects' blood sugar level will rise

\_\_

milligrams per deciliter less.

Identify slope: Identify the slope of the least squares regression line. $\newline$ The equation given is $y = -0.004x + 28.109$ . The slope of the least squares regression line is the coefficient of $x$ , which is $-0.004$ .
Interpret slope: Interpret the slope. $\newline$ In the equation $y = -0.004x + 28.109$ , $x$ represents the dose of the drug in milligrams, and $y$ represents the rise in blood sugar in milligrams per deciliter. The slope of $-0.004$ indicates that for each one milligram increase in the dose of the drug, the rise in blood sugar is predicted to decrease by $0.004$ milligrams per deciliter.

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