Question

melissa collected the data in the table.
when $x = 4$, what is the residual?
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$$\begin{tabular}{|c|c|c|c|} \\hline $x$ & given & predicted & residual \\\\ \\hline 1 & 2 & 1 & 1 \\\\ \\hline 2 & 3 & 4 & $-1$ \\\\ \\hline 3 & 8 & 7 & 1 \\\\ \\hline 4 & 9 & 10 & ? \\\\ \\hline \\end{tabular}$$

options: $-1$, $1$, $3$, $-3$

Explanation:

Step1: Recall residual formula

Residual is calculated as \( \text{Residual} = \text{Given value} - \text{Predicted value} \).

Step2: Identify values for \( x = 4 \)

For \( x = 4 \), the given value is \( 9 \) and the predicted value is \( 10 \).

Step3: Calculate residual

Substitute into the formula: \( \text{Residual} = 9 - 10 = -1 \).

Answer:

\(-1\)