standard normal distributions:
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The standard normal distribution is a probability distribution that associates 
       the normal random variable X with a cumulative probability . 
        The normal distribution is defined by the following equation: 
                    1                                     
           f(x) = --------- * exp(-0.5 *x^2)               
                   sqrt(2*pi)                                

    where f(x) is the density function, x is the input
       pi is 3.1415926

  Manually, we could calculate a few values. 
   x=0    -> f(x) = 1/sqrt(2*3.1415925) ->  0.3989423

   x=1    -> f(1) = 1/sqrt(2*3.1415926)*exp(-0.5) ->   0.2419707
  
   x=-1    -> f(-1) = 1/sqrt(2*3.1415926)*exp(-0.5*(-1)^2) ->   0.2419707

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T-value and P value
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 We should look at the T-value and/or P-value to make a judgement 
     whether a coefficient is statistically significant. 

 To get a critical T-value for a given alpha (significant level)
   and number of observations, we have the following formula 


  >   qt(0.05,50)    # for one sided 
      [1] -1.675905

  > qt(0.05/2,50)

  >  qt(0.05/2,50)
    [1] -2.008559


critical.t <- function(){
    cat('\n','Enter Alpha Level','\n')
    alpha<-scan(n=1,what = double(0),quiet=T)
    cat('\n','1 Tailed or 2 Tailed:\nEnter either 1 or 2','\n')
    tt <- scan(n=1,what = double(0),quiet=T)
    cat('\n','Enter Number of Observations','\n')
    n <- scan(n=1,what = double(0),quiet=T)
    cat('\n\nCritical Value =',qt(1-(alpha/tt), n-2), '\n')
}


source: https://stackoverflow.com/questions/11526041/critical-t-values-in-r

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R2 and adjusted R2
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  R2 is a measure of goodness of a model 

  adjusted R2 is a better measure since it considers 
     the number of independent variables. 

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adjusted beta
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The formula is used to adjust our estimated beta. 

                    2         1   
    adjusted Beta= ---*beta + --
                    3         3 
    where beta is our estimated beta

 The underlying logic is that beta has a meaning reverting property. 
     The mean is about 1. This means that if our estimated beta this 
     year is above 1, there is a good chance that its next year's beta 
     would be smaller. The opposite is true: if this year's beta is 
     less than 1, there is a good chance that the next year's beta 
     is higher, i.e., closer to 1. 

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