Question
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice,
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table.
Part 1
Height (in.) | Head Circumference (in.) | |
---|---|---|
27.75 | 17.5 | |
25.25 | 17 | |
26.25 | 17.2 | |
25.75 | 17 | |
27.5 | 17.5 | |
26.75 | 17.3 | |
26.25 | 17.1 | |
27 | 17.3 |
n | |
---|---|
3 | 0.997 |
4 | 0.950 |
5 | 0.878 |
6 | 0.811 |
7 | 0.754 |
8 | 0.707 |
9 | 0.666 |
10 | 0.632 |
11 | 0.602 |
12 | 0.576 |
13 | 0.553 |
14 | 0.532 |
15 | 0.514 |
16 | 0.497 |
17 | 0.482 |
18 | 0.468 |
19 | 0.456 |
20 | 0.444 |
21 | 0.433 |
22 | 0.423 |
23 | 0.413 |
24 | 0.404 |
25 | 0.396 |
26 | 0.388 |
27 | 0.381 |
28 | 0.374 |
29 | 0.367 |
30 | 0.361 |
n |
(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? Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.)
Part 5
(e) Convert the data to centimeters, and recompute the linear correlation coefficient. What effect did the conversion have on the linear correlation coefficient? Convert the first four data values to centimeters. | Height (centimeters) | Head Circumference (centimeters) | |
(Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.)
Part 6
Convert the last four data values to centimeters. | Height (centimeters) | Head Circumference (centimeters) | |
enter your response here | enter your response here | ||
enter your response here | enter your response here | ||
enter your response here | enter your response here | ||
enter your response here | enter your response here |
(Type integers or decimals. Do not round. List the terms in the same order as they appear in the original list.)
f) What is the new linear correlation coefficient? r=
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