r command for sxx

interestednew

New Member
what is the R command for SXX? cant seem to find it on google. thanks
and sxy while we are at it.

bryangoodrich

Probably A Mammal
Do you mean SSx? The sum of squares of x

$$= \sum (X - \overline{X})^2$$

and,

$$Sxy = \sum (X - \overline{X})(Y - \overline{Y})$$

interestednew

New Member
yes exactly. it is referred to as SXX and not SSX in my book, but the equations are the same.

Last edited:

Dason

There isn't something that directly gives it to you but it's pretty easy to program yourself
Code:
SXX <- sum((x - mean(x))^2)
# alternatively
SXX <- (length(x)-1)*var(x)

interestednew

New Member
Yeah haha I guess thats pretty trivial. I had one more R command question (for now anyway), I ran a linear regression in R and got the estimated intercept and slope. I know how to get their CI in R but I was wondering if there was a way to get CI for a specified X value. thanks

Dason

Use the "predict" function setting the "interval" parameter to "confidence". You can also get prediction intervals by setting interval to "prediction" instead.

interestednew

New Member
Ok thanks that got me going.....what I cant seem to do is use predict to get a confidence interval for an X value that is not part of my data.

Code:
predict(lm(Y~X),interval=c("confidence"),level=0.95)
say I want to predict x=4 (which is not one of my X values in the model)

bryangoodrich

Probably A Mammal
You have to specify the new data you want to predict by the "newdata" argument (see help file for details). Just remember, it needs to be a dataframe of the same variable. So if you have, for instance, Y ~ X, then you want to issue a command like

Code:
predict(lm(Y ~ X), newdata = data.frame(X = c(10, 20, 30)), int = "confidence", level = 0.90)
Otherwise, predict uses fitted values by default.

bryangoodrich

Probably A Mammal
Also, with respect to the sum of squared deviations mentioned earlier (and sxx is the notation), there are a number of matrix ways to get it. For instance, consider a Y vector of response values. You can get $$\sum Y^2$$ with

Code:
t(Y) %*% as.matrix(Y)
I don't have my book handy (just moved), but there are similar matrix methods to get the various sum of squares and squared deviations (from the mean) in a nice matrix form. You should be able to find it in any statistics book on regressions. It goes along with solving the normal equations.