Question

consider the table showing the given, predicted, and residual values for a data set.

x	given	predicted	residual
2	2.2	1.5	0.7
3	4.5	4.7	-0.2
4	6.1	6.7	-0.6

which point would be on the residual plot of the data?

• (1, -1.6)
• (2, 1.5)
• (3, 4.5)
• (4, -0.6)

Explanation:

Step1: Recall Residual Plot Points

A residual plot has points \((x, \text{Residual})\), where \(x\) is the independent variable and Residual is \( \text{Given} - \text{Predicted} \).

Step2: Check Each Option

• For \((1, -1.6)\): Residual at \(x = 1\) is \(-0.4\), not \(-1.6\). Incorrect.
• For \((2, 1.5)\): Residual at \(x = 2\) is \(0.7\), not \(1.5\). Incorrect.
• For \((3, 4.5)\): Residual at \(x = 3\) is \(-0.2\), not \(4.5\). Incorrect.
• For \((4, -0.6)\): Residual at \(x = 4\) is \(-0.6\). Correct.

Answer:

(4, -0.6)