Question

the equation of the regression line for the data in the table is $hat{y}=4.7x - 179$, where $x$ represents the height and $hat{y}$ is the predicted walking speed. student height (in) walking speed (m/min) alice 62 108 santiago 70 145 isaiah 73 159 elliot 68 143 alexis 64 117 lydia 66 132

Explanation:

1. Problem - likely to find the predicted walking speed for a given height:

• The regression - line equation is \(\hat{y}=4.7x - 179\), where \(x\) is the height and \(\hat{y}\) is the predicted walking speed.

Step1: Select a height value from the table (for example, let's take Alice's height \(x = 62\))

We want to find the predicted walking - speed for \(x = 62\).

Step2: Substitute \(x = 62\) into the regression equation

\(\hat{y}=4.7\times62-179\)
First, calculate \(4.7\times62\):
\(4.7\times62=(4 + 0.7)\times62=4\times62+0.7\times62=248 + 43.4 = 291.4\)
Then, subtract 179:
\(\hat{y}=291.4−179 = 112.4\)

Answer:

If we consider \(x = 62\) (Alice's height), the predicted walking speed \(\hat{y}=112.4\) m/min. (You can repeat this process for other height values in the table).