Question

A medical student reads that with enough sun exposure, the human body can manufacture vitamin D3. This sounds too amazing to be true, so she decides to test it out.
Over the next few weeks, she spends a varying number of hours in the sun, x. At the end of each week, she measures the concentration of vitamin D3 in her blood (in nanograms per milliliter), y.
The least squares regression line of this data set is:
y=8.728x–50.433
What concentration of vitamin D3 does this line predict if the student spends 6.74 hours in the sun per week?
Round your answer to the nearest thousandth.
nanograms

Answer 1

To predict the concentration of vitamin D3 using the least squares regression line given by the equation:

\[ y = 8.728x - 50.433 \]

we need to substitute \( x = 6.74 \) (the number of hours in the sun) into the equation.

Calculating \( y \):

\[
y = 8.728(6.74) - 50.433
\]

First, calculate \( 8.728 \times 6.74 \):

\[
8.728 \times 6.74 \approx 58.82672
\]

Now, substituting back into the equation:

\[
y \approx 58.82672 - 50.433
\]

Calculating the result:

\[
y \approx 8.39372
\]

Now rounding to the nearest thousandth:

\[
y \approx 8.394
\]

Thus, the predicted concentration of vitamin D3 is approximately **8.394 nanograms per milliliter**.