Question

maria gathered the data in the table. she finds the line of best fit to be $y = 2.78x - 4.4$. \

$$\begin{tabular}{|c|c|} \\hline $x$ & $y$ \\\\ \\hline 1 & $-2$ \\\\ \\hline 2 & $1.3$ \\\\ \\hline 3 & $4.2$ \\\\ \\hline 4 & $7.3$ \\\\ \\hline 5 & $8.9$ \\\\ \\hline \\end{tabular}$$

what is the residual value when $x = 4$? \bigcirc $-6.72$ \bigcirc $-0.58$ \bigcirc $0.58$ \bigcirc $6.72$

Explanation:

Step1: Find observed y at x=4

From the table, when $x=4$, $y_{\text{observed}} = 7.3$

Step2: Calculate predicted y at x=4

Substitute $x=4$ into $y=2.78x-4.4$:
$y_{\text{predicted}} = 2.78(4) - 4.4 = 11.12 - 4.4 = 6.72$

Step3: Compute residual value

Residual = $y_{\text{observed}} - y_{\text{predicted}}$
$\text{Residual} = 7.3 - 6.72 = 0.58$

Answer:

0.58 (Option C)