Question

consider the graph of the line of best fit, ( y = 0.5x + 1 ), and the given data points. which is the residual value when ( x = 2 )?

Explanation:

Step1: Find the predicted value

Substitute \(x = 2\) into the line - of - best - fit equation \(y=0.5x + 1\).

$$y_{predicted}=0.5\times2+1=1 + 1=2$$

Step2: Find the observed value

From the graph, when \(x = 2\), the observed \(y\) - value (\(y_{observed}\)) is \(1\).

Step3: Calculate the residual

The formula for the residual is \(Residual=y_{observed}-y_{predicted}\).

$$Residual = 1-2=-1$$

Answer:

\(-1\)