title: Interpreting standard error for similar (but different) specified linear regression models: R
body: <p>I get different standard error values depending on the way I specify a linear regression model (for categorical variable) in R.</p>
  <p>For example,</p>
  <pre><code>library(alr4)
  library(tidyverse)
  
  FactorModel &lt;- lm(I(log(acrePrice)) ~ I(as.factor(year)), data = MinnLand)
  summary(FactorModel)
  </code></pre>
  <p><a href="https://i.stack.imgur.com/ktZJ7.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ktZJ7.png" alt="Specifying a standard regression model" /></a></p>
  <p>However, if I specify a regression model with &quot;+0&quot;, the standard error (and consequently other values) are different.</p>
  <pre><code>FactorModel1 &lt;- lm(I(log(acrePrice)) ~ I(as.factor(year)) + 0, data = MinnLand)
  summary(FactorModel1)
  </code></pre>
  <p><a href="https://i.stack.imgur.com/R6tRK.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/R6tRK.png" alt="Adding +0 gives me a different result" /></a></p>
  <p>How do I know which one is the correct standard error? I kinda understand how to interpret the estimates. For instance, in the first model if I want to know the estimate of 2003, its intercept + the coefficient of 2003. However, in the second model, it automatically calculates the actual value.</p>
  <p>Is there a similar interpretation for standard error?</p>