Question

19. Height versus Head Circumference (Refer to Problem 27, Section 4.1.) A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data: Height (inches), x | Head Circumference (inches), y | Height (inches), x | Head Circumference (inches), y 27.75 | 17.5 | 26.5 | 17.3 24.5 | 17.1 | 27 | 17.5 25.5 | 17.1 | 26.75 | 17.3 26 | 17.3 | 26.75 | 17.5 25 | 16.9 | 27.5 | 17.5 27.75 | 17.6 Source: Denise Slucki, student at Joliet Junior College (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. (d) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above average or below average? (e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d). (f) Notice that two children are 26.75 inches tall. One has a head circumference of 17.3 inches; the other has a head circumference of 17.5 inches. How can this be? (g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why?

          19. Height versus Head Circumference (Refer to Problem 27, Section 4.1.) A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data:

Height (inches), x | Head Circumference (inches), y | Height (inches), x | Head Circumference (inches), y
27.75 | 17.5 | 26.5 | 17.3
24.5 | 17.1 | 27 | 17.5
25.5 | 17.1 | 26.75 | 17.3
26 | 17.3 | 26.75 | 17.5
25 | 16.9 | 27.5 | 17.5
27.75 | 17.6

Source: Denise Slucki, student at Joliet Junior College

(a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Use the regression equation to predict the head circumference of a child who is 25 inches tall.
(d) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above average or below average?
(e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d).
(f) Notice that two children are 26.75 inches tall. One has a head circumference of 17.3 inches; the other has a head circumference of 17.5 inches. How can this be?
(g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why?

19. Height versus Head Circumference (Refer to Problem 27, Section 4.1.) A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data:

Height (inches), x | Head Circumference (inches), y | Height (inches), x | Head Circumference (inches), y
27.75 | 17.5 | 26.5 | 17.3
24.5 | 17.1 | 27 | 17.5
25.5 | 17.1 | 26.75 | 17.3
26 | 17.3 | 26.75 | 17.5
25 | 16.9 | 27.5 | 17.5
27.75 | 17.6

Source: Denise Slucki, student at Joliet Junior College

(a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Use the regression equation to predict the head circumference of a child who is 25 inches tall.
(d) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above average or below average?
(e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d).
(f) Notice that two children are 26.75 inches tall. One has a head circumference of 17.3 inches; the other has a head circumference of 17.5 inches. How can this be?
(g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why?

Added by James G.

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