Question

a scatterplot consists of (1, 4.0), (2, 3.3), (3, 3.8), (4, 2.6), and (5, 2.7). the line of best fit used to model the data is y = -0.33x + 4.27. which residual plot is correct?

Explanation:

Step1: Recall the formula for residual

Residual = Observed - Predicted.

Step2: Calculate predicted values for each x

For \(x = 1\), \(y_{pred}=- 0.33\times1 + 4.27=3.94\). Residual \(=4.0 - 3.94 = 0.06\).
For \(x = 2\), \(y_{pred}=-0.33\times2 + 4.27=3.61\). Residual \(=3.3 - 3.61=- 0.31\).
For \(x = 3\), \(y_{pred}=-0.33\times3 + 4.27=3.28\). Residual \(=3.8 - 3.28 = 0.52\).
For \(x = 4\), \(y_{pred}=-0.33\times4 + 4.27=2.95\). Residual \(=2.6 - 2.95=-0.35\).
For \(x = 5\), \(y_{pred}=-0.33\times5 + 4.27=2.62\). Residual \(=2.7 - 2.62 = 0.08\).

Step3: Analyze the signs and magnitudes of residuals

The residuals are \(0.06,-0.31,0.52,-0.35,0.08\). We need to find the residual - plot where the points at \(x = 1,2,3,4,5\) have approximately these vertical - displacements from the \(x\) - axis.

Answer:

You need to check which of the given residual plots has points with \(y\) - values (residuals) close to \(0.06,-0.31,0.52,-0.35,0.08\) at \(x = 1,2,3,4,5\) respectively. Without specific labels for the plots, it's not possible to give a named answer, but the correct plot should have the above - calculated residual values at the corresponding \(x\) - positions.