Recursive regression in R

Question

Say I have a data frame in R as follows:

> set.seed(1)
> X <- runif(50, 0, 1)
> Y <- runif(50, 0, 1)
> df <- data.frame(X,Y)
> head(df)

         


        

Answer 1

Maybe this will be of help:

set.seed(1)
X1 <- runif(50, 0, 1)
X2 <- runif(50, 0, 10) # I included another variable just for a better demonstration
Y <- runif(50, 0, 1)
df <- data.frame(X1,X2,Y)


rolling_lms <- lapply( seq(20,nrow(df) ), function(x) lm( Y ~ X1+X2, data = df[1:x , ]) )

Using the above lapply function you the recursive regression you want with full information.

For example for the first regression with 20 observations:

> summary(rolling_lms[[1]])

Call:
lm(formula = Y ~ X1 + X2, data = df[1:x, ])

Residuals:
     Min       1Q   Median       3Q      Max 
-0.45975 -0.19158 -0.05259  0.13609  0.67775 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.61082    0.17803   3.431  0.00319 **
X1          -0.37834    0.23151  -1.634  0.12060   
X2           0.01949    0.02541   0.767  0.45343   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2876 on 17 degrees of freedom
Multiple R-squared:  0.1527,    Adjusted R-squared:  0.05297 
F-statistic: 1.531 on 2 and 17 DF,  p-value: 0.2446

And has all the info you need.

> length(rolling_lms)
[1] 31

It performed 31 linear regressions starting from 20 observations and until it reached 50. Every regression with all the information is stored as an element of the rolling_lms list.

EDIT

As per Carl's comment below, in order to get a vector of all the slopes for each regression, for X1 variable on this occasion, this is a very good technique (as Carl suggested):

all_slopes<-unlist(sapply(1:31,function(j) rolling_lms[[j]]$coefficients[2]))

Output:

> all_slopes
         X1          X1          X1          X1          X1          X1          X1          X1          X1          X1 
-0.37833614 -0.23231852 -0.20465589 -0.20458938 -0.11796060 -0.14621369 -0.13861210 -0.11906724 -0.10149900 -0.14045509 
         X1          X1          X1          X1          X1          X1          X1          X1          X1          X1 
-0.14331323 -0.14450837 -0.16214836 -0.15715630 -0.17388457 -0.11427933 -0.10624746 -0.09767893 -0.10111773 -0.06415914 
         X1          X1          X1          X1          X1          X1          X1          X1          X1          X1 
-0.06432559 -0.04492075 -0.04122131 -0.06138768 -0.06287532 -0.06305953 -0.06491377 -0.01389334 -0.01703270 -0.03683358 
         X1 
-0.02039574