Concept explainers
a)
To draw a
Given the data:
Speed | Stopping Distance |
10 | 15.1 |
20 | 39.9 |
30 | 75.2 |
40 | 120.5 |
50 | 175.9 |
Draw a scatter plot of the data:
The speed is represented along the
b)
To find a quadratic regression model of the data.
The quadratic curve that best fits the data:
Given the data:
Speed | Stopping Distance |
10 | 15.1 |
20 | 39.9 |
30 | 75.2 |
40 | 120.5 |
50 | 175.9 |
A calculator is used to find a quadratic curve that best fits the data:
The equation of the curve is found:
Conclusion:
The quadratic curve that best fits the data:
c)
Superimpose the regression curve, found in the previous part, in the scatter plot.
The regression curve
d)
To use the regression model to find the stopping distance of a vehicle travelling at a speed of
As per the regression model, the stopping distance of the vehicle travelling at a speed of
Found the regression mode:
Substitute
Thus,
Conclusion:
As per the regression model, the stopping distance of the vehicle travelling at a speed of
e)
To determine the speed predicted by the regression model when the stopping distance is
As per the regression model, the stopping distance of the vehicle will be
Found the regression model:
Substitute
Solve the equation
Conclusion:
Thus,
That is, as per the regression model, the stopping distance of the vehicle will be
Chapter 2 Solutions
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