Question

use the table to find the residual points.
which residual plot is the correct one for the data?

Explanation:

Step1: Recall Residual Formula

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

Step2: Calculate Residual for \( x = 1 \)

Given \( = -0.7 \), Predicted \( = -0.28 \)
\( \text{Residual} = -0.7 - (-0.28) = -0.7 + 0.28 = -0.42 \)

Step3: Calculate Residual for \( x = 2 \)

Given \( = 2.3 \), Predicted \( = 1.95 \)
\( \text{Residual} = 2.3 - 1.95 = 0.35 \)

Step4: Calculate Residual for \( x = 3 \)

Given \( = 4.1 \), Predicted \( = 4.18 \)
\( \text{Residual} = 4.1 - 4.18 = -0.08 \)

Step5: Calculate Residual for \( x = 4 \)

Given \( = 7.2 \), Predicted \( = 6.41 \)
\( \text{Residual} = 7.2 - 6.41 = 0.79 \)

Step6: Calculate Residual for \( x = 5 \)

Given \( = 8 \), Predicted \( = 8.64 \)
\( \text{Residual} = 8 - 8.64 = -0.64 \)

Answer:

For \( x = 1 \): \(-0.42\)
For \( x = 2 \): \(0.35\)
For \( x = 3 \): \(-0.08\)
For \( x = 4 \): \(0.79\)
For \( x = 5 \): \(-0.64\)

(To determine the correct residual plot, plot the points \((1, -0.42)\), \((2, 0.35)\), \((3, -0.08)\), \((4, 0.79)\), \((5, -0.64)\) and compare with the given plots.)