Chapter 5: Q. 59 (page 329)

Crawl before you walk (At what age do babies learn to crawl? Does it take
longer to learn in the winter, when babies are often bundled in clothes that restrict their
movement? Perhaps there might even be an association between babies’ crawling age and
the average temperature during the month they first try to crawl (around $6$ months after
birth). Data were collected from parents who brought their babies to the University of
Denver Infant Study Center to participate in one of a number of studies. Parents reported
the birth month and the age at which their child was first able to creep or crawl a distance
of $4$ feet within one minute. Information was obtained on $414$ infants $(208 b o y s a n d 206 g i r l s)$ . Crawling age is given in weeks, and average temperature (in degrees Fahrenheit) is
given for the month that is $6$ months after the birth month.
a. Make an appropriate graph to display the relationship between average temperature and
average crawling age. Describe what you see.
Some computer output from a least-squares regression analysis of the data is shown.
b. What is the equation of the least-squares regression line that describes the relationship
between average temperature and average crawling age? Define any variables that you
use.
c. Interpret the slope of the regression line.
d. Can we conclude that warmer temperatures $6$ months after babies are born causes them
to crawl sooner? Justify your answer.

Short Answer

Expert verified

a. we saw that there is a moderately strong, negative, linear association between the average temperature and average crawling age while the scatterplot also show an outlier.

b. $y = 35.68 - 0.0777 x$ , where x represents the average temperature and y represents the average crawling age.

c. the slope of the regression line is $- 0.0777$

d. No, we cannot conclude that warmer temperatures $6$ months after babies are born causes them

to crawl sooner.

Step by step solution

Part (a): Step 1: Given information

We have been given that parents reported the birth month and the age at which their child was first able to creep or crawl a distance of $4$ feet within one minute. this Information was obtained on $414$ infants $(208 b o y s a n d 206 g i r l s)$ .

We need to draw an appropriate graph to display the relationship between average temperature and average crawling age.

Part (a): Step 2: Explanation

The graph is shown below

This implies that there is a moderately strong, negative, linear association between the average temperature and average crawling age while the scatterplot also shows an outlier.

Part (b): Step 1: Given information

we need to find out the equation of the least-squares regression line that describes the relationship

between average temperature and average crawling age.

Part (b): Step 2: Explanation

General equation for least-squares regression line is

$y = b_{0} + b_{1} x$

from the above given table of constants

$b_{0} = 35.68 b_{1} = - 0.0777 n o w r e p l a c i n g v a l u e s o f b_{0} a n d b_{1} i n t h e e q u a t i o n y = b_{0} + b_{1} x y = 35.68 - 0.0777 x$

where x represents the average temperature and y represents the average crawling age.

Part (c): Step 1: Given information

We need to find the slope of regression line.

Part (c): Step 2: Explanation

The equation of the regression line is

$y = 35.68 - 0.0777 x$

slope is the coefficient of x in the regression line.

slope $= {b_{1}}_{} = - 0.0777$

Part (d): Step 1: Given information

we need to check that Can we conclude that warmer temperatures months after babies are born cause them to crawl sooner.

Part (d): Step 2: Explanation

As we concluded that there is a moderately strong, negative, linear association between the average temperature and average crawling age and this implies that an increase in the average temperature does not necessarily cause a decrease in the average crawling age.