It's similar to the post https://stats.stackexchange.com/questions/5135/interpretation-of-rs-lm-output?newreg=537edb7e3e574479ba4efe796cfa22b5. 

    lm(formula = iris$Sepal.Width ~ iris$Petal.Width)


however, just a point that I can't understand for the explanation of t-value. 

[![enter image description here][2]][2]


It shows that, t-value is the ratio from the first two values 
      
    t-value = estimate_mean/std.error

Questions: Is this t-value exactly the t-score in student's t distribution? 


Based on my understanding, from the definition, t-score is calculated as follows. 
[![enter image description here][3]][3]


If assuming a null hypothesis that response residual mean is 0, the correct t-score in this lm() case, in my understanding, should be as follows. 

     t-score given H_null = estimated_mean / (std.error/sqrt(n)) 
                          = sqrt(n) * estimated_mean/std.error

**Therefore, t-score I derived is sqrt(n) times larger than t-value given by lm() ....** Any one know which part is wrong above? Thanks!

  [1]: https://i.sstatic.net/pECRg.png
  [2]: https://i.sstatic.net/Ge7gI.png
  [3]: https://i.sstatic.net/cexOF.png