Lm in R does not give coefficients for all levels of factors in categorical data

Question

I tested linear regression using R using categorical attributes and observed that I did not get the coefficient value for each of the different factor factors that I have.

Please see my code below, I have 5 factor levels for states, but see only 4 coefficient values.

> states = c("WA","TE","GE","LA","SF") > population = c(0.5,0.2,0.6,0.7,0.9) > df = data.frame(states,population) > df states population 1 WA 0.5 2 TE 0.2 3 GE 0.6 4 LA 0.7 5 SF 0.9 > states=NULL > population=NULL > lm(formula=population~states,data=df) Call: lm(formula = population ~ states, data = df) Coefficients: (Intercept) statesLA statesSF statesTE statesWA 0.6 0.1 0.3 -0.4 -0.1 

I also tried with a large dataset by following these steps, but still see the same behavior

 for(i in 1:10) { df = rbind(df,df) } 

EDIT: Thanks to the answers from eipi10, MrFlick and the economy. Now I understand that one of the levels is used as a control level. But when I get new test data whose state value is "GE", how can I replace in the equation y = m1x1 + m2x2 + ... + c?

I also tried to smooth the data so that each of these factor levels gets a separate column, but again for one of the columns I get NA as a coefficient. If I have new test data whose state is "WA", how can I get a "population value"? What can I replace as a coefficient?

 > df1 

population GE MI TE WA 1 1 0 0 0 1 2 2 1 0 0 0 3 2 0 0 1 0 4 1 0 1 0 0

lm (formula = population ~ (GE + MI + TE + WA), data = df1)

 Call: lm(formula = population ~ (GE + MI + TE + WA), data = df1) Coefficients: (Intercept) GE MI TE WA 1 1 0 1 NA 

Answer 1

GE dropped alphabetically as a term for interception. As stated in eipi10, you can interpret the coefficients for other levels in states with GE , since the baseline ( statesLA = 0.1 means that LA is on average 0.1 times larger than GE).

EDIT:

To answer the updated question:

If you include all levels in a linear regression, you will have a situation called perfect collinearity, which is responsible for the strange results that you see when you insert each category into your own variable. I won’t explain it, just find the wiki and find out that linear regression doesn’t work if the variable coefficients are fully represented (and you also expect the interception time). If you want to see all levels in a regression, you can perform a regression without the term of interception, as suggested in the comments, but again, this is not recommended unless you have specific reasons.

Regarding the interpretation of GE in your equation y=mx+c , you can calculate the expected y , knowing that the levels of other states are binary (zero or one), and if the state is GE, they will all be zero.

eg.

 y = x1b1 + x2b2 + x3b3 + c y = b1(0) + b2(0) + b3(0) + c y = c 

If you do not have other variables, as in the first example, the GE effect will be equal to the interception term (0.6).