Question

A linear regression was performed using the following five data points: $A(2,22),B(10,4),C(6,14),D(14,2),E(18,-4).$The residual for which of the five points has The largest absolute value?

a. A

b. B

c. C

d. D

e. E

Short answer

$C$point has the largest absolute value.

Step-by-step solution

Given Information

We are given five data points and we have to find that point which has largest absolute value.

Explanation

First we have to plot the graph of given points then we see that it is linearly decreasing graph of Slope $$\begin{gathered} \mathrm{m}=-\frac{18}{8} \\ \mathrm{m}=-2.25 \end{gathered}$$

And the equation of graph is $\mathrm{y}=-2.25\mathrm{x}+26.5$now we have to find the values at points.

$\mathrm{y}\left(2\right)=22,\mathrm{y}\left(10\right)\hspace{0.17em}=4,\mathrm{y}\left(6\right)=13,\mathrm{y}\left(14\right)=-5,\mathrm{y}\left(18\right)=-14$

We know that $Residual=observed-predicted$

Hence for each y:$$\begin{gathered} \left(1\right)22-22=0 \\ \left(2\right)4-4=0 \\ \left(3\right)14-13=1 \\ \left(4\right)2+5=7 \\ \left(5\right)-4+14=10 \end{gathered}$$

Hence we see that E point having maximum residual absolute value.