To find the residual for the point [tex]\((5, 1)\)[/tex] given the line of best fit [tex]\( y = -0.2x + 1.7 \)[/tex], follow these steps:
1. Identify the coordinates of the point: The given point is [tex]\((5, 1)\)[/tex], where [tex]\( x = 5 \)[/tex] and [tex]\( y_{\text{observed}} = 1 \)[/tex].
2. Use the line of best fit equation to find the predicted [tex]\( y \)[/tex] value:
[tex]\[
y = -0.2x + 1.7
\][/tex]
Substituting [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[
y_{\text{predicted}} = -0.2 \times 5 + 1.7
\][/tex]
Calculate the value:
[tex]\[
y_{\text{predicted}} = -1 + 1.7 = 0.7
\][/tex]
3. Calculate the residual: The residual is calculated as the difference between the observed [tex]\( y \)[/tex] value and the predicted [tex]\( y \)[/tex] value:
[tex]\[
\text{Residual} = y_{\text{observed}} - y_{\text{predicted}}
\][/tex]
Substituting the values:
[tex]\[
\text{Residual} = 1 - 0.7 = 0.3
\][/tex]
Therefore, the residual for the point [tex]\((5, 1)\)[/tex] is [tex]\( 0.3 \)[/tex].
The correct answer is B. 0.3.
