Dummy Variables and coding reasons A ran a regression analysis predicting Salary from gender. In the data Female was coded as 2 and male was coded as 1. Then I was asked to change females to -1 and male to 5. In the analyis ɑ, b, t,and SEb changed. 
Why? What is the reasoning behind the coding system here?
 A: It is hard to see without further information why one would lie to code a binary variable as $(-1,5)$, but it is fairly easy to see how the coefficient changes with a simple experiment:
lets create a random data.frame in R with 100 observations, where salary has a mean of 60K with a standard deviation of 15K:
   set.seed(10)
df <- data.frame(salary = rnorm(100, mean = 60000, sd = 15000), gender = rbinom(100, 1, 0.42))
df$gender5 <- ifelse(df$gender == 0, -1, 5)

Now gender is coded $(0,1)$ and gender5 is coded $(-1,5)$. Lets regress salary with gender with the original encoding and with the new one:
Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    61291       1994  30.736   <2e-16 ***
gender         -6421       2765  -2.322   0.0223 *  

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  60220.7     1692.1  35.589   <2e-16 ***
gender5      -1070.2      460.9  -2.322   0.0223 * 

So:
coefficient: The coefficient has a simple meaning always - whats the average difference in salary between the two categories. The first coding $(0,1)$ is very intuitive and so is used often, and is easily understood when viewed through the regression equation: $\hat{salary}=61,291-6,421\times gender$. If males are coded $1$ and females $0$, than males predicted average salary is $61,421-6,421\times 1=54,870$ or simply $6,421$$ less than females. 
When the coding changes, so does the meaning. Now instead a gap of $1$, we have a gap of $6$. Now if we want to predict men, we will do: $\hat{salary}=60,220.7-1,070.2\times 5 = 54,870$. Exactly the same (with a rounding error). The gap is not $1$ now, but $6$. Multiplying slope coefficient by $6$, e.g., $-1,070.2\times 6=-6,421$ and we arrive back at the slope coefficient using the first coding scheme $(0,1)$. This is just much less intuitive to calculate.
Standard Error: Same shtick. The $s.e.$ is dependent on the distribution. if you change it, you change the deviation. so $2765/6=460.9$
T and significance value: Should not change. If it did, there probably is a problem somewhere. re-coding the variables changes the coefficients, but not the significance values.
