SE of the mean

To get the SE of the mean at a particular set of X values we will need to use regular SAS. If the X values are not part of the original data then we need to add them to our data set. For example, in the Red Spruce problem, we need the SE of the mean at an elevation of 1500 meters above sea level for northern sites. X1 = 1 and X2 = 1500. We need to add this line to our data set, but since we do not have a data point with these values, the Y variable is missing. In SAS a missing value is denoted by a ".". To read in the data we would enter:

data sasuser.rwg102;
input LOC ELEV DAMAGE;
datalines; 
0        1615           5       
0        1768          13       
0        1524           6       
          .
          .
          .
1        1000       42
1        1060       58
1        1120       24
1        1500        .
run;

NOTE: the ... in the middle just represents skipped lines to shorten the page. The last line corresponds to our value for the new prediction. Since the Y value is missing, this extra line is not included in the regression calculations.

To get the SE, let's use PROC REG. In the program editor, enter:

PROC REG data=sasuser.rwg102;
	model DAMAGE = LOC ELEV / cli clm;
	run;

The "/ cli clm" is an option to the model statement which tells says to compute a confidence and prediction interval for each case in the data set. (these are 95% intervals, but you will have the SE and prediction so it is straightforward to calculate the 99% interval by hand. The output will show up in the SAS OUTPUT window.

The column labeled Std Err Predict is really the Standard error of the mean for the regression at each set of X values. You will still have to use your calculator if you want the SE for the "prediction" as opposed to the mean. Remember SE(predicting a new obs) = sqrt(MSE + SE(mean)^2). (You don;t have to do this now; it is just for future reference.)

You can use this to verify your calculations (SHOW your work) for the SE of the mean and 95% CI for part3(b). The output should be:


Predict   Std Err  Lower95%  Upper95%
  Value   Predict      Mean      Mean

74.8361     7.853   59.1327   90.5395

( You will still have to calculate the 99% CI by hand :-)