Technology: Regression and Correlation

Let's use the TI-84 to perform the computations related to regression and correlation for the size and 2007 assessed value data from the property tax data set:

house	size	assess	lot	taxes	stories
20911	1561	304	0.2	2604	1
20912	1038	297.6	0.2	280	1
20918	1224	289.5	0.17	2353	1
20921	1232	292.8	0.17	756	1
20924	1995	314.6	0.17	2620	2
20927	1714	322.7	0.18	2632	1
20930	1832	336.1	0.18	2779	2
21003	1095	279	0.18	2321	1
21006	2011	319.5	0.18	2663	2
21015	1366	289.3	0.18	2415	1
21018	1292	301.4	0.18	2477	1
21023	1458	314.3	0.18	1386	1
21028	2031	320.9	0.18	2676	2
21105	1366	304	0.18	2473	1

First, enter the data into two lists; here I'll use L1 for size and L2 for assessed value:

enter size data in L1 and assess data in L2

just like we did when creating a scatterplot:

scatterplot of size vs. assess

In the scatterplot, we see a reasonably linear association between size and assessed value, with no noticeable outliers so it is appropriate to find a regression line and compute correlation. You should always check a scatterplot first before doing any computations.

After graphing the scatterplot, QUIT the graphing mode (press 2ND and MODE) and then press STAT, move the cursor to CALC and move the cursor down to 8:LinReg(a+bx):

press STAT then move cursor to CALC and down to LinReg(a+bx)

press ENTER, then type L1 followed by , (a comma) and then L2:

press ENTER then type L1 a comma and L2, then press ENTER

Now press ENTER. You should get a screen that looks like this:

linear regression output for size vs. assess

You should notice the regression equation (the calculator calls the intercept a and the slope b), which we can write as: `hat(text(assess)) = 248.96 + 0.03777 times text(size)`

The number r is the correlation and r² tells us that about 67% of the variation in assessed value can be explained by the variation in size.

If you don't see r and r² on you calculator, do the following: press 2ND and then 0 to get to the CATALOG menu:

press 2ND and 0 to get to the catalog menu

Now scroll down (or press the x^-1 key, which has a green D above it, to skip to the D entries, then scroll down) until you see DiagnosticOn:

scroll down to DiagnosticOn and press ENTER twice

and press ENTER twice. You should see this:

after pressing ENTER twice this should appear

Now run LinReg(a+bx) again. The calculator should always tell you the value of r and r² from now on, at least until you take the batteries out of your calculator.

You may notice that there is a LinReg(ax+b) listed in the CALC menu along with LinReg(a+bx). Both of these will give us the same information, but let's stick with LinReg(a+bx) since it matches the order in which we will write the regression equation in this course.

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