Question

In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).

Answer 1

The closer this value is to 1 or -1, the better the fit. For linear, the correlation coefficient R2=.96. For quadratic, the R2=.99. For exponential, the R2=.91. This means quadratic is the best fit, very good actually since .99 is very close to 1.

Explanation:

Answer 2

When you have a set of data points and you want to get a model out of it, you do data fitting. The first thing to do is plot the points using a scatter plot type of chart as shown in the picture. I used MS Excel as a tool for data fitting. On the left side of the picture, I used linear fitting. Then, it gives you the linear equation y=0.2907x + 2.2643. It has a correlation coefficient, R^2, of 0.9595. This measures how good your data fits the model equation. The closer it is to 1, the better. However, it is rare to get 1 because that is very ideal. A R^2 of 0.9595 is very satisfactory already. But if you want an even better model, the right side of the picture shows data fitting on a quadratic equation with an equation of y=0.0209x^2 +0.506x+2.0232 with R^2 of 0.9992.