Thursday, August 31, 2006

Straightening data

Here's the plan we developed in class:

Load your (x,y) data into L1 and L2.
Look at them.

If they are not already straight, figure out if the ideal model would pass through the x-axis, the y-axis, or both. To save some time, try this to straighten your data:

Case 1: if the ideal model would cross the y-axis, take the ln of the observed y values. Case 2: if the model would cross the x-axis, take the ln of the x values, too.

THEN
Case 1: Run the linear regression on the original x and the ln y. Change your stat plot to show the (x, ln y) points with the linear regression equation. If this is a good fit, then the residuals will be scattered. Correct the linear regression equation to reflect that the y-values were really ln y. Solve the fixed equation for y.

Case 2: Run the linear regression on the ln x and the ln y. Change your stat plot to show the (ln x, ln y) points with the linear regression equation. If this is a good fit, then the residuals will be scattered. Correct the linear regression equation to reflect that the y-values were really ln y and the x-values were really ln x. Solve the corrected equation for y.

To check your results, put the new equation for y into the y= register to graph. Change your statplot to show the original data (x,y), probably in L1 and L2. The curve you generated should pass neatly through the data.

Note that this method finds the line which miniomizes the sum of the squared residuals from the STRAIGHTENED data, not the squares of the residuals from the curved fit.




Oh yeah, go Braves!

Tuesday, August 15, 2006

Welcome to the new school year

How is a permutation different from a combination? How are they similar?