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 accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. X + (Round the slope to three decimal places and round the constant to one decimal place as needed.)

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12:51
K
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
accompanying data. Complete parts (a) through (g) below.
Click the icon to view the children's data.
Data Table
(a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the
response variable.
y = x+
(Round the slope to three decimal places and round the constant to one decimal place as needed.)
Height (inches), x Head Circumference (inches), y
27.5
17.4
24.5
17.0
25.75
17.0
26
17.5
24.25
16.8
27.75
17.5
26.25
17.2
17.4
17.2
17.4
17.4
27.25
26.5
26.5
27.75
Vol) 1
LTE2
=
Print
ا... ا...
Done
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X
Transcribed Image Text:12:51 K 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 accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. Data Table (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. y = x+ (Round the slope to three decimal places and round the constant to one decimal place as needed.) Height (inches), x Head Circumference (inches), y 27.5 17.4 24.5 17.0 25.75 17.0 26 17.5 24.25 16.8 27.75 17.5 26.25 17.2 17.4 17.2 17.4 17.4 27.25 26.5 26.5 27.75 Vol) 1 LTE2 = Print ا... ا... Done 45% X
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 accompanying data. Complete
parts (a) through (g) below.
Click the icon to view the children's data.
Interpret the y-intercept, if appropriate. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. For a height of 0 inches, the head circumference is predicted to be
in.
(Round to three decimal places as needed.)
OB. For every inch increase in head circumference, the height increases by in., on average.
(Round to three decimal places as needed.)
OC. For every inch increase in height, the head circumference increases by in., on average.
g
(Round to three decimal places as needed.)
OD. For a head circumference of 0 inches, the height is predicted to be in
(Round to three decimal places needed)
OE. It is not appropriate to interpret the y-intercept.
(c) Use the regression equation to predict the head circumference of a child who is 25 inches tall.
y=in
(Round to two decimal places as needed.)
(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 or below the value predicted by the regression model?
The residual for this observation is, meaning that the head circumference of this child is the value predicted by the regression model.
(Round to two decimal places as needed.)
(e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d). Choose the correct graph below.
Click to select your answer(s).
?
Transcribed Image Text: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 accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. Interpret the y-intercept, if appropriate. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For a height of 0 inches, the head circumference is predicted to be in. (Round to three decimal places as needed.) OB. For every inch increase in head circumference, the height increases by in., on average. (Round to three decimal places as needed.) OC. For every inch increase in height, the head circumference increases by in., on average. g (Round to three decimal places as needed.) OD. For a head circumference of 0 inches, the height is predicted to be in (Round to three decimal places needed) OE. It is not appropriate to interpret the y-intercept. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. y=in (Round to two decimal places as needed.) (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 or below the value predicted by the regression model? The residual for this observation is, meaning that the head circumference of this child is the value predicted by the regression model. (Round to two decimal places as needed.) (e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d). Choose the correct graph below. Click to select your answer(s). ?
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