The table below shows the heights of 6 pairs of brothers and sisters, labeled A through F. Heights are rounded to the nearest inch.

[tex]
\[
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
& \multicolumn{6}{|c|}{Pair} \\
\hline
& A & B & C & D & E & F \\
\hline
Brother's height (inches) & 68 & 70 & 68 & 71 & 69 & 71 \\
\hline
Sister's height (inches) & 64 & 66 & 65 & 71 & 66 & 67 \\
\hline
\end{tabular}
\]
[/tex]

The line of best fit for this data is [tex]y = 1.42105x - 32.2632[/tex].

For the brother and sister whose heights are both 71 inches, what is the difference between the sister's actual height and the height predicted by the line of best fit?

[tex]\square[/tex]

To solve this problem, we're going to compare the actual height of the sister to the height predicted by the line of best fit for the one brother and sister pair whose heights are both 71 inches.

1. Identify the data needed:
- Brother's height: 71 inches
- Actual sister's height: 71 inches

2. Use the line of best fit to find the predicted sister's height:
- The equation of the line of best fit is [tex]\( y = 1.42105x - 32.2632 \)[/tex].
- Plug the brother's height (71 inches) into the equation:
[tex]\[
\text{Predicted sister's height} = 1.42105 \times 71 - 32.2632
\][/tex]

3. Calculate the predicted sister's height:
- Perform the multiplication:
[tex]\[
1.42105 \times 71 = 100.89555
\][/tex]
- Next, subtract 32.2632:
[tex]\[
100.89555 - 32.2632 = 68.63135
\][/tex]
- Therefore, the predicted sister's height is approximately 68.63135 inches.

4. Determine the difference between the actual and predicted heights:
- The actual sister's height is 71 inches.
- Subtract the predicted height from the actual height:
[tex]\[
71 - 68.63135 = 2.36865
\][/tex]

So, the difference between the sister's actual height and the height predicted by the line of best fit is approximately 2.37 inches.