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Concept explainers
a
To find: A linear model for the data.
a
![Check Mark](/static/check-mark.png)
Answer to Problem 148RE
The regression line is
Explanation of Solution
Given: The following ordered pairs ( x,y ) represents Olympic year x and winning time y (in minutes) in the men’s 400-meter freestyle swimming event.
Calculation:
The equation for the regression line is given below.
Calculation: Let x =8 corresponding to year 1968 then the above ordered pairs can be written as below table.
Year x | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 |
Winning Time t | 4.150 | 4.005 | 3.866 | 3.855 | 3.854 | 3.783 | 3.750 | 3.800 | 3.677 | 3.718 | 3.698 | 3.669 |
Using linear regression calculator on above result data table, linear regression line is,
The regression coefficient is -0.9013.
b
To graph: A
b
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given: The following ordered pairs ( x,y ) represents Olympic year x and winning time y (in minutes) in the men’s 400-meter freestyle swimming event.
Calculation:
Let x =8 corresponding to year 1968 then the above ordered pairs can be written as below table.
Year x | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 |
Winning
Time t | 4.150 | 4.005 | 3.866 | 3.855 | 3.854 | 3.783 | 3.750 | 3.800 | 3.677 | 3.718 | 3.698 | 3.669 |
Graph:
Scatter plot for the above table data is shown below.
Conclusion: The regression model is the good fit for data.
c
To find: the good fit for the data.
c
![Check Mark](/static/check-mark.png)
Answer to Problem 148RE
The regression model is the good fit for data.
Explanation of Solution
Given: The following ordered pairs ( x,y ) represents Olympic year x and winning time y (in minutes) in the men’s 400-meter freestyle swimming event.
Calculation:
The regression coefficient is -0.9013.
So, regression model is the good fit for data because regression coefficient is -0.9013. which is close to -1.
Thus, the regression model is the good fit for data.
d.
To find: the model appropriate for predicting the winning times in future Olympic or not.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 148RE
Yes, this model appropriate for predicting the winning times in future Olympic.
Explanation of Solution
Given: The following ordered pairs ( x,y ) represents Olympic year x and winning time y (in minutes) in the men’s 400-meter freestyle swimming event.
Calculation:
Regression line is
The regression coefficient is -0.9013.
Regression model is the good fit for data because regression coefficient is -0.9013. It is close to -1.
Since Regression model is the good fit for data because regression coefficient is -0.9013. it is close to -1. So, this model appropriate for predicting the winning times in future Olympic.
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS:GRAPH.APPROACH
- 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
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