The article "Application of Genetic Algorithms to Optimum Design of Elasto-damping Elements of a Half-Car Model Under Random Road Excitations" (M. Mirzael and R. Hassannejad, Proceedings of the Institution of Mechanical Engineers, 2007:515-526) presents values of a coefficient (y), a unitless quantity that measures the road impact on an automobile suspension, and the time (t ) for the car to travel a distance equal to the length between the front and rear axles. The results are as follows:
|
t
|
y
|
t
|
y
|
t
|
y
|
|
0.0
|
1.000
|
0.5
|
0.995
|
1.0
|
0.987
|
|
0.1
|
0.999
|
0.6
|
0.993
|
1.1
|
0.985
|
|
0.2
|
0.998
|
0.7
|
0.992
|
1.2
|
0.983
|
|
0.3
|
0.997
|
0.8
|
0.990
|
1.3
|
0.981
|
|
0.4
|
0.996
|
0.9
|
0.988
|
1.4
|
0.979
|
a. Compute the least-squares line for predicting road impact (y) from time (t). Plot the residuals versus the fitted values.
b. Compute the least-squares line for predicting ln y from t . Plot the residuals versus the fitted values.
c. Compute the least-squares line for predicting y from t 1.5 . Plot the residuals versus the fitted values.
d. Which of the three models (a) through (c) fits best? Explain.
e. Using the best model, estimate the road impact for a time of 0.75.