Question

Use the least squares regression line of this data set to predict a value.
On today's episode of Science Time with Adele, Adele demonstrates that walking speed affects how wet a person will get in the rain. She simulates walking through the rain at various speeds.
Adele keeps track of her walking speed (in meters per second), x. Next, she measures how wet she is by taking the difference of her weight before and after walking through the rain (in kilograms), y.
Walking speed Amount of water
1.0 1.7
1.2 1.4
1.5 0.8
1.6 0.3
1.7 0.3
The least squares regression line of this data set is:
y=
–
2.147x+3.906
If Adele walks through the rain at 1.5 meters per second, how much water does this line predict she would soak up?
Round your answer to the nearest thousandth.

Answer 1

To predict how much water Adele would soak up while walking at a speed of 1.5 meters per second using the least squares regression line \( y = -2.147x + 3.906 \), we can substitute \( x = 1.5 \) into the equation.

\[
y = -2.147(1.5) + 3.906
\]

Calculating the first part:

\[
-2.147 \times 1.5 = -3.2205
\]

Now, add 3.906:

\[
y = -3.2205 + 3.906 = 0.6855
\]

Rounding to the nearest thousandth, we have:

\[
y \approx 0.686
\]

Thus, the predicted amount of water Adele would soak up while walking at 1.5 meters per second is approximately **0.686 kilograms**.