Finding the First y-Differences of a Set of Data
When the x-differences are all constant, then the y-differences (or first differences) are useful in telling if a set of data is nearly linear or not.
To find the first y-differences, press STAT, select 1:EDIT by pressing ENTER. Enter the x values in L1, and the y values in L2 as shown below.
Next, with the flashing cursor in the L3 column, press the UP ARROW once so that L3 is highlighted. Press 2nd LIST[STAT] and RIGHT ARROW to OPS menu.
From the OPS menu select 7: by pressing a 7. now appears at the bottom of the screen beside L3=. Press 2nd L2 to type L2, and then press the ) key. Press ENTER and the y-differences will appear in the L3 column.
Examining the y-differences in L3 column, we see that the data are all exactly equal to each either. This means that the data is exactly linear.