Question

the line of best fit to model the data in the table is ( y = 5.2x - 0.4 ). what is the residual for 5? -1.6 -0.6 0.6 1.6

Explanation:

Step1: Recall residual formula

Residual is calculated as \( \text{Residual} = \text{Observed } y - \text{Predicted } y \).

Step2: Find predicted \( y \) when \( x = 5 \)

The line of best fit is \( y = 5.2x - 0.4 \). Substitute \( x = 5 \) into the equation:
\( y = 5.2(5) - 0.4 = 26 - 0.4 = 25.6 \).

Step3: Find observed \( y \) when \( x = 5 \)

From the table, when \( x = 5 \), the observed \( y \) is 24.

Step4: Calculate the residual

Using the residual formula: \( \text{Residual} = 24 - 25.6 = -1.6 \).

Answer:

-1.6