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Answer :
We start with the information that for this pair both the brother's and sister's actual heights are [tex]$71$[/tex] inches. The line of best fit is given by
[tex]$$
y = 1.42105x - 32.2632,
$$[/tex]
where [tex]$x$[/tex] is the brother's height and [tex]$y$[/tex] is the predicted sister's height.
1. Substitute the brother's height ([tex]$x = 71$[/tex]) into the equation to find the predicted sister's height:
[tex]$$
y = 1.42105(71) - 32.2632.
$$[/tex]
2. With the calculation, we find that the predicted sister's height is approximately:
[tex]$$
y \approx 68.63135\text{ inches}.
$$[/tex]
3. Next, we find the difference between the actual sister's height and the predicted sister's height. The actual sister's height is [tex]$71$[/tex] inches. Thus, the difference is:
[tex]$$
\text{Difference} = |71 - 68.63135| \approx 2.36865\text{ inches}.
$$[/tex]
Therefore, the sister's actual height is about [tex]$2.37$[/tex] inches different from what the line of best fit predicts.
[tex]$$
y = 1.42105x - 32.2632,
$$[/tex]
where [tex]$x$[/tex] is the brother's height and [tex]$y$[/tex] is the predicted sister's height.
1. Substitute the brother's height ([tex]$x = 71$[/tex]) into the equation to find the predicted sister's height:
[tex]$$
y = 1.42105(71) - 32.2632.
$$[/tex]
2. With the calculation, we find that the predicted sister's height is approximately:
[tex]$$
y \approx 68.63135\text{ inches}.
$$[/tex]
3. Next, we find the difference between the actual sister's height and the predicted sister's height. The actual sister's height is [tex]$71$[/tex] inches. Thus, the difference is:
[tex]$$
\text{Difference} = |71 - 68.63135| \approx 2.36865\text{ inches}.
$$[/tex]
Therefore, the sister's actual height is about [tex]$2.37$[/tex] inches different from what the line of best fit predicts.
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