Points and their residual values are shown in the table.

\begin{tabular}{|c|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] & Residual \\
\hline
1 & 2 & -0.4 \\
\hline
2 & 3.5 & 0.7 \\
\hline
3 & 5 & -0.2 \\
\hline
4 & 6.1 & 0.19 \\
\hline
5 & 8 & -0.6 \\
\hline
\end{tabular}

Which residual value is the farthest from the line of best fit?

A. 0.19
B. 0.7
C. -0.4
D. -0.6



Answer :

To determine which residual value is the farthest from the line of best fit, we first need to compute the absolute values of the given residuals.

Residuals provided:
- -0.4
- 0.7
- -0.2
- 0.19
- -0.6

Step 1: Calculate the absolute values of each residual:
- The absolute value of -0.4 is 0.4.
- The absolute value of 0.7 is 0.7.
- The absolute value of -0.2 is 0.2.
- The absolute value of 0.19 is 0.19.
- The absolute value of -0.6 is 0.6.

Step 2: Compare these absolute values to find the largest one:

From the absolute values:
- 0.4
- 0.7
- 0.2
- 0.19
- 0.6

We see that 0.7 is the largest absolute value.

Therefore, the residual value that is the farthest from the line of best fit is 0.7.

Answer: 0.7