Question

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.

Height (inches), x	Head Circumference (inches), y
28	17.7
24.25	17.3
25.5	17.2
25.75	17.7
24.5	17.0
28.25	17.8
26.75	17.5
27.25	17.5
26.75	17.5
26.75	17.7
27.5	17.7

(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

24.5 inches tall.

(d) Compute the residual based on the observed head circumference of the 24 .5 ​-inch-tall child in the table. Is the head circumference of this child above or below the value predicted by the regression​ model?

(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 17.5 ​inches; the other has a head circumference of 17.7 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?

Answer 1

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