I a Multiple linear regression model, from published literature, I am implementing a spreadsheet to generate new predictions based on the published model. the literature stated Coefficients and the error in each as well as the RMS error. However to estimate prediction interval i need to know the matrix (X'X)^-1 Where X is a k+1 by N model matrix. and X' it the transpose of X
As per http://www.stats.uwo.ca/faculty/braun/ss3859/chapters/chapter_4/ch4.pdf (Slide 45)
So, I downloaded the training set of data from the supplementary data, and tried to make my own X matrix. However, I have tried inverting (X'X) in both excel and R without success. Excel gives me garbage output while R gives me a singularity error. However, if I eliminate the "column of one's" from the X matrix making it an k by X matrix, now (X'X) inverts just fine.
Just to see what is going on, I've also tried feeding the training set of points into Excel's Linnest function as well as R's lm , and I get a model out of both with co-efficient s that are very close to the published literature models. So this makes me think the matrix shouldn't have any issues like this.
Also note, the model has 5 quantitative and 1 qualitative dimension (with 42 possible results), so final model has 49 dimensions.
So I am wondering where I went wrong? why is my X'X matrix not invertible when I include the column of ones?