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.

Options

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.

Solution Preview

Calculations are in the attached excel file.

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

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... MPG = 53.5094 - 0.2666 *Horse Power For a unit increase in horse power, the MPG ... Thus 76.06 % variability in MPG can be explained by the regression model. ...

...regression results in terms of the signs of the coefficients, the statistical significance of the coefficients and the explanatory power of the regression (R2 ...