Concept explainers
a
To find: A linear model for the data.
a
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
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
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.
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
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