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Fitting Equations to Data

Fitting an equation to data is the process of finding a linear, quadratic, exponential, or any other sort of function whose graph includes, or comes as close as possible to, a given set of data in the form of ordered pairs.

The relative predictive power of a model shows how accurately the model is related to the data.

Example :

Plot the set of data points below. Determine whether to use a linear , quadratic , or exponential regression equation. Find the regression equation and graph it.

( 0 , 0.75 ) , ( 0.25 , 0.81 ) , ( 0.5 , 0.9 ) , ( 0.75 , 1.02 ) , ( 1 , 1.2 ) ( 1.25 , 1.4 ) , ( 1.5 , 1.56 ) , ( 1.75 , 1.7 ) , ( 2 , 1.9 )

Solution

Enter the x and y -coordinates in your calculator and plot the points.

The points seem to approach x -axis asymptotically. So, we assume an exponential model.

Use your calculator to determine the equation of the exponential regression of the points plotted.

The equation of the function is y = 0.7275 ( 1.6333 ) x .

Graph the function with the equation y = 0.7275 ( 1.6333 ) x .