When you finish going over these instructions, do TEXT problem #5 ( "stories" and "height of building") in Ch. 12. One of the points is an outlier.

This explains how to find outliers on various calculators. Suppose the data is (3, 5), (6, 8), (9,7), (5, 20). The xlist is 3, 6, 9, 5 and the ylist is 5, 8, 7, 20. Put the xlist into L1 and the ylist into L2. Do the linear regression. yhat = 11.2267 - .2133x

NOTE: TI-89: Use Flashapps to enter your lists and then find your instructions below the instructions for the TI-83 & 86.

FOR TI-83 & 86 CALCULATORS:

Arrow to the list name L4. Enter L2-L3. Press Enter. (In L4 are the y - yhat values.)

Arrow to the list name L5. Enter L4^2. Press Enter. (In L5 are the (y - yhat)^2 values.)

Continue by finding the Instructions for the appropriate calculator below (83 or 86):

FOR TI-83:

Exit to the Home Screen. Clear it. Press 2nd LIST. Arrow to MATH. Press 5:sum. (Press L5). Press Enter. You should see 137.1467 (to 4 decimal places). This is the SSE.

Calculate s. Press the square root symbol and enter (137.1467/2). (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter. You should see 8.2809 (to 4 decimal places).

Multiply 8.2809 by 1.9. You should see 15.7337.

Press L4. Press Enter. (Use the arrow keys to scroll through the list.)

Compare 15.7337 to the absolute values of the numbers in L4. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier.

Absolute values of the numbers in L4 are 5.587, 1.947, 2.307, 9.8398. None of them are greater than 15.7337, so no point is an outlier.

FOR TI-86:

Exit to the Home Screen. Clear it. Press 2nd LIST. Press F5 (OPS). Press MORE. Press F1 (sum). Press 2nd F3 (NAMES). Find the F key with L5 and press it. Press Enter. You should see 137.1467 (to 4 decimal places). This is the SSE.

Calculate s. Press the square root symbol and enter (137.1467/2). (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter. You should see 8.2809 (to 4 decimal places).

Multiply 8.2809 by 1.9. You should see 15.7337.

Press L4. Press Enter. (Use the arrow keys to scroll through L4.)

Compare 15.7337 to the absolute values of the numbers in L4. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier.

Absolute values of the numbers in L4 are 5.587, 1.947, 2.307, 9.8398. None of them are greater than 15.7337 so no point is an outlier.

FOR THE TI-89:

NOTE: When you do Linear Regression, a list called "resid" is created automatically.
This list has the y - yhat values in it.

Go into Flashapps and into your lists. Arrow to "resid" so you see it. Then arrow to the list name L3. Press F3. Press 1:names. Arrow down to STATVARS. If it is not checked, press F4. Then arrow down to resid. Press Enter. Press ^2. L3 will have the (y - yhat)^2 values. Press HOME and Press F1 8 to clear it. Press 2nd MATH. Press 3:List. Press 6:Sum. Press alpha L3). Depending on how you have MODE Display Digits set, you should see approximately 137.1467. This is the SSE.

Calculate s. (You should be HOME.) Press clear. Press the square root symbol and enter 137.1467/2). (You get the denominator by taking the number of data points and subtracting 2: 4 - 2 = 2.) Press Enter.
You should see 8.2809 (to 4 decimal places).

Press the times key and enter 1.9. Press Enter. You should see 15.7337

Press clear. Press 2nd VAR-LINK. Arrow down to resid (It is below STAT VARS). Press Enter. Arrow up to the list. Scroll through the list using the arrow keys.

Compare 15.7337 to the absolute values of the numbers in the list. If any absolute value is greater than or equal to 15.7337, then the corresponding point is an outlier.

Absolute values of the numbers in the list are approximately 5.59, 1.95, 2.31, 9.84. None of them are greater than 15.7337 so no point is an outlier.

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