Question

zane keeps track of his walking speed (in meters per second), x. next, he measures how wet he is by taking the difference of his weight before and after walking through the rain (in kilograms), y. the least squares regression line of this data set is: y = -1.538x + 2.487 if zane walks through the rain at 0.91 meters per second, how much water does this line predict he would soak up? round your answer to the nearest thousandth. kilograms

Explanation:

Step1: Substitute \(x = 0.91\) into the regression equation

We have the regression equation \(y=-1.538x + 2.487\). Substitute \(x = 0.91\) into it:
\(y=-1.538\times0.91+2.487\)

Step2: Calculate the value of \(y\)

First, calculate \(-1.538\times0.91=-1.538\times(0.9 + 0.01)=-1.538\times0.9-1.538\times0.01=-1.3842-0.01538=-1.39958\)
Then, \(y=-1.39958 + 2.487\)
\(y = 1.08742\)

Step3: Round to the nearest thousandth

Rounding \(1.08742\) to the nearest thousandth (three - decimal places). Since the fourth decimal digit is \(4\lt5\), we keep the third decimal digit as it is.

Answer:

\(1.087\)