Concept explainers
a
To draw
a
Explanation of Solution
Given information:
Graph:
Interpretation:
Using a graphic utility, the scatter plot for the given data is shown above.
b
To find if the scatter plot could be modeled by linear model, quadratic model or neither.
b
Answer to Problem 12E
Linear model
Explanation of Solution
Given information:
To determine if the given graph can be modeled by linear model, quadratic model or neither of them, try to draw a straight line or a parabola through the given scatter plot.
If a straight line can be drawn through the points of the scatter plot, it could be modelled by linear model whereas if a parabola can be drawn through the points of the scatter plot, it could be modelled by a quadratic model.
In case if both are not possible, it could neither be modeled.
Here, in the given graph we could draw a straight line. Therefore, the scatter plot could be modeled by a linear model.
Conclusion:
Therefore, given scatter plot is modeled by linear model.
c
To find a model for the data using regression feature of a graphing utility.
c
Answer to Problem 12E
Linear model
Explanation of Solution
Given information:
Calculation:
Using the graphic utility to find the regression,
Conclusion:
Therefore, from the above figure. the regression equation for the linear model is
d
To draw the model with the scatter plot from subpart (a) using a graphic utility.
d
Explanation of Solution
Given information:
Graph:
Interpretation:
Using a graphic utility, a straight line is formed when the data is kept on a graph.
e
To draw a table comparing the original data with the data given by the model.
e
Explanation of Solution
Given information:
Table:
Draw the table comparing the original data and the data given by the model.
Original data | Data from the model | ||
x | y | ||
0 | 6140 | 0 | 7467.76 |
2 | 6815 | 2 | 7394.456 |
4 | 7335 | 4 | 7321.152 |
6 | 7710 | 6 | 7247.847 |
8 | 7915 | 8 | 7174.543 |
10 | 7590 | 10 | 7101.239 |
12 | 7975 | 12 | 7027.935 |
14 | 7700 | 14 | 6954.631 |
16 | 7325 | 16 | 6881.326 |
18 | 6820 | 18 | 6808.022 |
20 | 6125 | 20 | 6734.718 |
22 | 5325 | 22 | 6661.414 |
Data from the model is obtained by substituting the values of x as
Interpretation:
When the original data and the data from the model are compared with each other, it is found that the values are nearly equal.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning