Concept explainers
a.
Construct a scatter plot for given data.
a.
Answer to Problem 30CT
Explanation of Solution
Given information:
Income generated from 2011 to 2017.
Year | Revenue |
2011 | 66.1 |
2012 | 116.9 |
2013 | 197.5 |
2014 | 325.9 |
2015 | 644.7 |
2016 | 846.6 |
2017 | 1076.8 |
Assume t=1 at 2011.
b.
Suitable Model for the data and coefficient of determination.
b.
Answer to Problem 30CT
The equation of linear model is
The coefficient of determination is 0.94.
Explanation of Solution
Given information:
Year | Revenue |
2011 | 66.1 |
2012 | 116.9 |
2013 | 197.5 |
2014 | 325.9 |
2015 | 644.7 |
2016 | 846.6 |
2017 | 1076.8 |
Formula used:
Coefficient of determination
Mean of x is 4
Mean of y is 467.7.
X | Y | X - Mx | Y - My | ( X - Mx)2 | ( X - Mx)( Y - My) |
1 | 66.1 | -3 | -401.686 | 9 | 1205.0571 |
2 | 116.9 | -2 | -350.886 | 4 | 701.7714 |
3 | 197.5 | -1 | -270.286 | 1 | 270.2857 |
4 | 325.9 | 0 | -141.886 | 0 | 0 |
5 | 644.7 | 1 | 176.9143 | 1 | 176.9143 |
6 | 846.6 | 2 | 378.8143 | 4 | 757.6286 |
7 | 1076.8 | 3 | 609.0143 | 9 | 1827.0429 |
Linear regression equation:
Where,
The equation of linear model is
Coefficient of determination:
X | Y | X2 | Y2 | XY |
1 | 66.1 | 1 | 4369.21 | 66.1 |
2 | 116.9 | 4 | 13665.61 | 233.8 |
3 | 197.5 | 9 | 39006.25 | 592.5 |
4 | 325.9 | 16 | 106210.8 | 1303.6 |
5 | 644.7 | 25 | 415638.1 | 3223.5 |
6 | 846.6 | 36 | 716731.6 | 5079.6 |
7 | 1076.8 | 49 | 1159498 | 7537.6 |
The coefficient of determination:
The coefficient of determination is 0.94.
c.
Construct the graph with the help of graphing utility.
c.
Answer to Problem 30CT
Explanation of Solution
Given information:
The equation of linear model is
The graph of
d.
Whether the model is fit for data or not.
d.
Answer to Problem 30CT
Yes, the model is fit for data.
Explanation of Solution
As
As
Chapter 3 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