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 )? -2 -1 1 2

Explanation:

Step1: Recall residual formula

Residual is observed \( y \) minus predicted \( y \). Formula: \( \text{Residual} = y_{\text{observed}} - y_{\text{predicted}} \).

Step2: Find predicted \( y \) at \( x = 2 \)

Given line of best fit: \( y = 0.5x + 1 \). Substitute \( x = 2 \):
\( y_{\text{predicted}} = 0.5(2) + 1 = 1 + 1 = 2 \).

Step3: Determine observed \( y \) at \( x = 2 \)

From the graph, at \( x = 2 \), the data point has \( y = 1 \) (observed \( y_{\text{observed}} = 1 \)).

Step4: Calculate residual

Substitute into residual formula:
\( \text{Residual} = 1 - 2 = -1 \).

Answer:

\(-1\) (corresponding to the option: \(-1\))