Concept explainers
(a)
To find:The linear regression equation for the given data.
(a)
Answer to Problem 46E
The linear regression equation for the given data is
Explanation of Solution
Given information:The table given below shows the ages and weights of nine girls:
Girl’s ages and weights | |
Age (months) | Weight (pounds) |
19 | 22 |
21 | 23 |
24 | 25 |
27 | 28 |
29 | 31 |
31 | 28 |
34 | 32 |
38 | 34 |
43 | 39 |
Calculation:
To find the linear regression equation of the given data, use graphing calculator.
Step 1: Press
Step 2: List the input values 19, 21, 24, 27, 29, 31, 34, 38 and 43 in the L1 column.
Step 3: List the input values 22, 23, 25, 28, 31, 28, 32, 34 and 39 in the L2 column.
Step 4: Press the keystrokes
Therefore, thelinear regression equation for the given data is
(b)
To find: The slope of the regression line for the given data and describe the representation of the slope.
(b)
Answer to Problem 46E
The slope of the regression line for the given data is 0.68 and it represents the average weight in pounds per month gain in girls from 1 to 4 years old.
Explanation of Solution
Given information:The table given below shows the ages and weights of nine girls:
Girl’s ages and weights | |
Age (months) | Weight (pounds) |
19 | 22 |
21 | 23 |
24 | 25 |
27 | 28 |
29 | 31 |
31 | 28 |
34 | 32 |
38 | 34 |
43 | 39 |
Calculation:
From part (a), the linear regression equation for the given data is
It is known that slope-form of a line is
Therefore, the slope of the regression line for the given data is 0.68 and it represents the average weight in pounds per month gain in girls from 1 to 4 years old.
(c)
To plot: The graph of the linear regression equation on a
(c)
Explanation of Solution
Given information:The table given below shows the ages and weights of nine girls:
Girl’s ages and weights | |
Age (months) | Weight (pounds) |
19 | 22 |
21 | 23 |
24 | 25 |
27 | 28 |
29 | 31 |
31 | 28 |
34 | 32 |
38 | 34 |
43 | 39 |
Graph:
To make the scatter plot enter the data, then follow the stepsusing graphing calculator.
Step 1: Press
Step 2: Press
Step 3: Press the keystrokes
Figure (1)
Interpretation:From the graph it can be interpreted that the weight of girls is increasing as there is increasing.
(d)
To find: The weight of 30 month old girl by using the regression equation.
(d)
Answer to Problem 46E
The approximate weight of 30 month old girl is 29.4 pounds.
Explanation of Solution
Given information:The table given below shows the ages and weights of nine girls:
Girl’s ages and weights | |
Age (months) | Weight (pounds) |
19 | 22 |
21 | 23 |
24 | 25 |
27 | 28 |
29 | 31 |
31 | 28 |
34 | 32 |
38 | 34 |
43 | 39 |
Calculation:
From part (a), the linear regression equation for the given data is
To find the weight of 30 month old girl, substitute 30 for
Therefore, the approximate weight of 30 month old girl is 29.4 pounds.
Chapter 1 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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