Question

Use the least squares regression line of this data set to predict a value.
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.
Dosage Rise in blood sugar level
148 29.56
320 28.45
351 27.07
364 29.60
498 17.61
796 19.46
The least squares regression line of this data set is:
y=
–
0.019x+33.293
What rise in blood sugar does this line predict for a subject who has a meal after taking 712 milligrams of the drug?
Round your answer to the nearest thousandth.
milligrams per deciliter

Answer 1

To predict the rise in blood sugar for a dosage of 712 milligrams using the least squares regression line formula \( y = -0.019x + 33.293 \), we will substitute \( x = 712 \) into the equation.

Calculating:

\[
y = -0.019(712) + 33.293
\]

Now, perform the multiplication:

\[
-0.019 \times 712 = -13.528
\]

Next, add this to 33.293:

\[
y = -13.528 + 33.293 = 19.765
\]

Therefore, the predicted rise in blood sugar is:

\[
\boxed{19.765} \text{ milligrams per deciliter}
\]

This rounded to the nearest thousandth is indeed 19.765.