Question

a data set is shown in the table. the line of best fit modeling the data is y = 2.69x - 7.95.

x	y
2	-3.2
3	1.0
4	2.3
5	5.6

what is the residual value when x = 3?

• -0.88
• -0.12
• 0.12
• 0.88

Explanation:

Step1: Recall residual formula

Residual = Observed \( y \) - Predicted \( y \).

Step2: Find predicted \( y \) at \( x = 3 \)

Use the line of best fit \( y = 2.69x - 7.95 \). Substitute \( x = 3 \):
\( y = 2.69(3) - 7.95 = 8.07 - 7.95 = 0.12 \).

Step3: Find observed \( y \) at \( x = 3 \)

From the table, when \( x = 3 \), observed \( y = 1.0 \).

Step4: Calculate residual

Residual = \( 1.0 - 0.12 = 0.88 \)? Wait, no—wait, residual is observed - predicted. Wait, no: Residual = Observed \( y \) - Predicted \( y \). Wait, observed \( y \) is 1.0, predicted is 0.12? Wait, no, wait: \( 2.69*3 = 8.07 \), \( 8.07 - 7.95 = 0.12 \). Observed \( y \) is 1.0. So residual = \( 1.0 - 0.12 = 0.88 \)? Wait, no, wait the options have 0.88? Wait, no, wait I think I messed up. Wait, \( 2.69*3 = 8.07 \), \( 8.07 - 7.95 = 0.12 \). Observed \( y \) is 1.0. So residual is \( 1.0 - 0.12 = 0.88 \)? Wait, but let me check again. Wait, the line of best fit is \( y = 2.69x - 7.95 \). For \( x = 3 \), predicted \( y = 2.69*3 - 7.95 = 8.07 - 7.95 = 0.12 \). Observed \( y \) is 1.0. So residual = observed - predicted = \( 1.0 - 0.12 = 0.88 \). Wait, but the options include 0.88. Wait, but let me check the calculation again. \( 2.69*3 = 8.07 \), \( 8.07 - 7.95 = 0.12 \). Observed \( y \) is 1.0. So \( 1.0 - 0.12 = 0.88 \). So the residual is 0.88.

Answer:

0.88