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Question

At a recent football game you noticed that students tend to be near the same height as their parent of the same gender. You surveyed several students and their parents and recorded the data below.

Student’s Height (in.)Parent’s Height (in.)61566257636265666560666667686863686970717268717373677471\begin{matrix} \text{Student's Height (in.)} & \text{Parent's Height (in.)}\\ \text{61} & \text{56}\\ \text{62} & \text{57}\\ \text{63} & \text{62}\\ \text{65} & \text{66}\\ \text{65} & \text{60}\\ \text{66} & \text{66}\\ \text{67} & \text{68}\\ \text{68} & \text{63}\\ \text{68} & \text{69}\\ \text{70} & \text{71}\\ \text{72} & \text{68}\\ \text{71} & \text{73}\\ \text{73} & \text{67}\\ \text{74} & \text{71}\\ \end{matrix}

Tyler's father came to pick him up and you asked his height. He is 6 feet tall. What is his residual and where does the data point lie in relation to the best-fit line?

Solution

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Determine the residual of the height if the actual height is 72 inches.

residual=actual valuepredicted value=7268.117susbtitute for the given values=3.883 inchesresidual in height\begin{align*} \text {residual} & = \text {actual value} - \text {predicted value} \\ & = 72 - 68.117 && {\text {susbtitute for the given values}} \\ & = 3.883 \text { inches} && {\text {residual in height}} \end{align*}

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