Question

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

$x$	$y$
2	$1.3$
3	$4.2$
4	$7.3$
5	$8.9$

what is the residual value when $x = 4$?
options: $0.58$, $-6.72$, $6.72$, $-0.58$

Explanation:

Step1: Recall residual formula

Residual is actual \( y \) minus predicted \( y \), i.e., \( \text{Residual} = y_{\text{actual}} - y_{\text{predicted}} \).

Step2: Find predicted \( y \) at \( x = 4 \)

Given line of best fit \( y = 2.78x - 4.4 \). Substitute \( x = 4 \):
\( y_{\text{predicted}} = 2.78(4) - 4.4 \)
Calculate \( 2.78 \times 4 = 11.12 \), then \( 11.12 - 4.4 = 6.72 \).

Step3: Find actual \( y \) at \( x = 4 \)

From the table, when \( x = 4 \), \( y_{\text{actual}} = 7.3 \).

Step4: Calculate residual

\( \text{Residual} = 7.3 - 6.72 = 0.58 \).

Answer:

\( 0.58 \)