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Solved: Height versus Head Circumference(Refer to versus
Chapter 3, Problem 19AYU(choose chapter or problem)
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects eleven 3-year-old children from her practice, measures their heights and head circumference, and obtains the data shown in the table on the next page.
(a) If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable.
(b) Draw a scatter diagram.
(c) Compute the linear correlation coefficient between the height and head circumference of a child.
(d) Does a linear relation exist between height and head circumference?
(e) Convert the data to centimeters (1 inch=2.54 cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation coefficient?
Questions & Answers
QUESTION:
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects eleven 3-year-old children from her practice, measures their heights and head circumference, and obtains the data shown in the table on the next page.
(a) If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable.
(b) Draw a scatter diagram.
(c) Compute the linear correlation coefficient between the height and head circumference of a child.
(d) Does a linear relation exist between height and head circumference?
(e) Convert the data to centimeters (1 inch=2.54 cm), and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation coefficient?
ANSWER:Step 1 of 6
Given:
The pediatrician has randomly selected eleven 3-year-old children.
She measured their heights and head circumferences
The data for height (x) and head circumference (y) is as follows:
\(\begin{array}{|c|c|} \hline \text { Height }(x) & \text { Head Circumference }(y) \\ \hline 27.75 & 17.5 \\ \hline 24.5 & 17.1 \\ \hline 25.5 & 17.1 \\ \hline 26 & 17.3 \\ \hline 25 & 16.9 \\ \hline 27.75 & 17.6 \\ \hline 26.5 & 17.3 \\ \hline 27 & 17.5 \\ \hline 26.75 & 17.3 \\ \hline 26.75 & 17.5 \\ \hline 27.5 & 17.5 \\ \hline \end{array}\)