# 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.

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#### 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.