Data Science Done Right (the Kitchen Style) #6

Let’s implement univariate multivariable linear regression (see derivations in previous chapter) in R the way it is usually used, i.e. mapping our dataset A not just to an element of the Quotient space Yl, but, after that, mapping it back into original space X. Our ks_lm0 R function is presented in Appendix 1.

Let’s run it against a dataset we used in one of the Statistical Methods classes (Statistical hypotheses testing for Diabetes Type II risk factors), also, for comparison, running these data through the standard lm function, making sure that results do match:

> load(url(“http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/diabetes.sav”))

> ks_lm0( diabetes, c(“chol”), c(“glyhb”,”ratio”,”bp.1s”,”bp.1d”) )
[,1]
[1,] 1.5868593
[2,] 11.2724797
[3,] 0.1593560
[4,] 0.3243256
[5,] 98.7703565

> cols <- c(“chol”,”glyhb”,”ratio”,”bp.1s”,”bp.1d”)
> clean2.diabetes <- diabetes[complete.cases(diabetes[,cols]),cols]
> View(clean2.diabetes)
> lmodel <- lm(“chol ~ glyhb + ratio + bp.1s + bp.1d”, clean2.diabetes)
> lmodel

Call:
lm(formula = “chol ~ glyhb + ratio + bp.1s + bp.1d”, data = clean2.diabetes)

Coefficients:
(Intercept) glyhb ratio bp.1s bp.1d
98.7704 1.5869 11.2725 0.1594 0.3243

Which, of course (no rocket science there, just simple matrix arithmetic), they do 🙂

However, let’s not stop here, and continue visualizing and playing with our data further…

 

Appendix 1

ks_lm0 <- function (df, yname, xnames){
all.names = c( unlist(yname), unlist(xnames) )
clean.df <- df[complete.cases( df[, all.names] ), all.names]

x <- clean.df
x[, yname] <- NULL
x[, ncol(clean.df)] <- rep_len(1, nrow(clean.df))

y <- clean.df[, yname]

#X <- matrix(unlist(x), nrow(x))
X <- matrix(do.call(cbind,x), nrow(x))

solve(t(X) %*% X) %*% t(X) %*% y
}

 

Advertisements
This entry was posted in Data Science Done Right and tagged , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s