title: What is the difference between Multiple R-squared and Adjusted R-squared in a single-variate least squares regression?
body: <p>Could someone explain to the statistically naive what the difference between <code>Multiple R-squared</code> and <code>Adjusted R-squared</code> is?  I am doing a single-variate regression analysis as follows:</p>
  
  <pre><code> v.lm &lt;- lm(epm ~ n_days, data=v)
   print(summary(v.lm))
  </code></pre>
  
  <p>Results:</p>
  
  <pre><code>Call:
  lm(formula = epm ~ n_days, data = v)
  
  Residuals:
      Min      1Q  Median      3Q     Max 
  -693.59 -325.79   53.34  302.46  964.95 
  
  Coefficients:
              Estimate Std. Error t value Pr(&gt;|t|)    
  (Intercept)  2550.39      92.15  27.677   &lt;2e-16 ***
  n_days        -13.12       5.39  -2.433   0.0216 *  
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
  
  Residual standard error: 410.1 on 28 degrees of freedom
  Multiple R-squared: 0.1746,     Adjusted R-squared: 0.1451 
  F-statistic: 5.921 on 1 and 28 DF,  p-value: 0.0216 
  </code></pre>