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    Power regression

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    This question concers the following data lists

    x 3 4 5 6 7 9 10
    y 4.6 4.0 3.6 3.3 3.0 2.7 2.5

    It is thought that x and y are related by a power relationship, that is, a function of the form y=ax^b.

    Perform power regression on these data, and then choose the one option describing a situation which these data could represent.

    You should assume in each case that appropriate units have been chosen for x and y, and that the values are quoted to an appropriate accuracy;you should consider only whether or not the power function you have found is appropriate to the situation.


    A. X is the time since a pebble was dropped down a well, and y is the distance it has fallen.

    B. x is the distance a pebble has fallen, and y is the time since it was dropped.

    C. x is the height and y is the radius of a 200ml cylindrical can.

    D. x is the radius and y is the height of a 200lm cylindrical can.

    E. x is the time and y is the distance from home for someone travelling towards their home at constant speed.

    F. x is the time taken to walk between two villages, and y is the average speed of the walker.

    G. x is the age of a wooden carving, and y is the amount of radioactive carbon in the carving.

    H. x is the amount of radioactive carbon in a carving, and y is its age.

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    Solution Preview

    Calculations are in the attached excel file.

    The function is y=8.0109 * X ^(-0.5003) approximately y ...

    Solution Summary

    Performs power regression