To determine the residual value at [tex]\( x = 3 \)[/tex] given the line of best fit [tex]\( y = 1.6x - 4 \)[/tex], we need to follow these steps:
1. Calculate the predicted [tex]\( y \)[/tex]-value using the line of best fit equation for [tex]\( x = 3 \)[/tex].
[tex]\[
y_{\text{predicted}} = 1.6 \cdot 3 - 4
\][/tex]
Solving this, we get:
[tex]\[
y_{\text{predicted}} = 4.8 - 4 = 0.8
\][/tex]
2. Identify the actual [tex]\( y \)[/tex]-value from the table for [tex]\( x = 3 \)[/tex]. The table tells us that:
[tex]\[
y_{\text{actual}} = -1
\][/tex]
3. Calculate the residual. The residual is the difference between the actual [tex]\( y \)[/tex]-value and the predicted [tex]\( y \)[/tex]-value:
[tex]\[
\text{Residual} = y_{\text{actual}} - y_{\text{predicted}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Residual} = -1 - 0.8 = -1.8
\][/tex]
Therefore, the residual value when [tex]\( x = 3 \)[/tex] is [tex]\( -1.8 \)[/tex]. Hence, the correct answer is:
[tex]\[ \boxed{-1.8} \][/tex]
