Concept explainers
a
To draw scatter plot using a graphic utility for the data provided.
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 14E
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 14E
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 | ||
-6 | 10.7 | -6 | 10.68181 |
-4 | 9.0 | -4 | 8.896966 |
-2 | 7.0 | -2 | 7.112118 |
0 | 5.4 | 0 | 5.32727 |
2 | 3.5 | 2 | 3.542422 |
4 | 1.7 | 4 | 1.757574 |
6 | -0.1 | 6 | -0.02727 |
8 | -1.8 | 8 | -1.81212 |
10 | -3.6 | 10 | -3.59697 |
12 | -5.3 | 12 | -5.38182 |
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)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning