R Linear Regression Data in Single Column - r

Question

I have the following data as an example:
InputName InputValue Output
===================================
Oxide 35 0.4
Oxide 35.2 0.42
Oxide 34.6 0.38
Oxide 35.9 0.46
CD 0.5 0.42
CD 0.48 0.4
CD 0.56 0.429
I want to do a linear regression of InputValue vs. Output treating different InputName as independent predictors.
If I want to use lm(Output ~ Oxide + CD) in R, it assumes a separate column for each predictor. In the example above that would mean making a separate column for Oxide and CD. I can do that using cast function from plyr package which might introduce NAs in the data.
However, is there a way to direct tell lm function that the input predictors are grouped according to the column InputName, and the values are given in the column Inputvalue?

Answer 1

It seems to me you are describing a form of dummy variable coding. This is not necessary in R at all, since any factor column in your data will automatically be dummy coded for you.
Recreate your data:
dat <- read.table(text="
InputName InputValue Output
Oxide 35 0.4
Oxide 35.2 0.42
Oxide 34.6 0.38
Oxide 35.9 0.46
CD 0.5 0.42
CD 0.48 0.4
CD 0.56 0.429
", header=TRUE)
Now build the model you described, but drop the intercept to make things a little bit more explicit:
fit <- lm(Output ~ InputValue + InputName - 1, dat)
summary(fit)
Call:
lm(formula = Output ~ InputValue + InputName - 1, data = dat)
Residuals:
1 2 3 4 5 6 7
-0.003885 0.003412 0.001519 -0.001046 0.004513 -0.014216 0.009703
Coefficients:
Estimate Std. Error t value Pr(>|t|)
InputValue 0.063512 0.009864 6.439 0.00299 **
InputNameCD 0.383731 0.007385 51.962 8.21e-07 ***
InputNameOxide -1.819018 0.346998 -5.242 0.00633 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.009311 on 4 degrees of freedom
Multiple R-squared: 0.9997, Adjusted R-squared: 0.9995
F-statistic: 4662 on 3 and 4 DF, p-value: 1.533e-07
Notice how all of your factor levels for InputName appear in the output, giving you a separate estimate of the effect of each level.
Concisely, the information you need are in these two lines:
InputNameCD 0.383731 0.007385 51.962 8.21e-07 ***
InputNameOxide -1.819018 0.346998 -5.242 0.00633 **

Answer 2

Here are 2 ways of doing this, split the data and do the regressions separately, or use interaction terms to specify that you want to consider the different levels of InputName to have separate slopes:
Split
lapply(split(dat,dat$InputName),lm,formula=Output~InputValue)
$CD
Call:
FUN(formula = ..1, data = X[[1L]])
Coefficients:
(Intercept) InputValue
0.2554 0.3135
$Oxide
Call:
FUN(formula = ..1, data = X[[2L]])
Coefficients:
(Intercept) InputValue
-1.78468 0.06254
Interaction
lm(Output~InputName + InputName:InputValue - 1,dat)
Call:
lm(formula = Output ~ InputName + InputName:InputValue - 1, data = dat)
Coefficients:
InputNameCD InputNameOxide InputNameCD:InputValue InputNameOxide:InputValue
0.25542 -1.78468 0.31346 0.06254
For comparision purposes I've also removed the intercept. Note that the estimated coefficients are the same in each case.