Multiple Regression, R output how to interpret the intercept

Question

1. In the example linear regression below, how do I interpret the (Intercept) with this R output?

A) Does the (Intercept) line represent pop1?

B) Does the Estimate column indicate the slope or the intercept for the (Intercept)? I get the irony of this question as it is called the intercept, but the numbers seems to indicate that the (Intercept) line represents the significance of slope for pop1 but I am not certain if is this correct so I have to ask.

> #in this example there are 6 doses given to 3 populations and sampled for an outcome.
> pop <- as.factor (c(1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3))
> test.doses <- c(0, 1, 2, 4, 8, 16)
> dose <- c(test.doses, test.doses, test.doses)
> outcome <- c(1, 2, 3, 5, 6, 7, 2, 3, 6, 7, 7, 6, 2, 2, 2, 2, 2, 2)
> 
> Model <- lm (outcome ~ dose * pop)
> summary (Model)

Call:
lm(formula = outcome ~ dose * pop)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.1714 -0.7569  0.0000  0.7781  2.0581 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  2.17143    0.74992   2.896  0.01344 * 
dose         0.35392    0.09948   3.558  0.00394 **
pop2         2.00000    1.06055   1.886  0.08375 . 
pop3        -0.17143    1.06055  -0.162  0.87428   
dose:pop2   -0.16129    0.14068  -1.147  0.27393   
dose:pop3   -0.35392    0.14068  -2.516  0.02712 * 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.338 on 12 degrees of freedom
Multiple R-squared:  0.7369,    Adjusted R-squared:  0.6273 
F-statistic: 6.722 on 5 and 12 DF,  p-value: 0.003318
```

Answer 1

Yes, R's output multiple regression can be tricky to understand at first.
Think about this way when pop =1 (the first categorical value) you can drop all of the terms with pop2 and pop3 so you linear regression equation is:

response =  2.17 + 0.35 *dose

Now if pop =2 you need to add the terms for which contain the pop2.

response =  2.17 + 0.35 *dose + (2.0 + -0.16*dose)
         or (2.17 + 2.0) + (0.35 -.16) *dose

And do the same when pop=3. Add the pop3 terms and drop the pop2 terms:

response =  2.17 + 0.35 *dose + (-0.17 + -.35 * dose)
         or (2.17 -.17) + (0.35 - .35) *dose

So all put together your equation is:

response =  2.17 + 0.35 *dose + 
            (2.0 + -0.16*dose)[When pop=2] + 
            (-0.17 + -.35 * dose)[When pop=3]

So in this case you have 3 different intercepts and 3 different slopes to correspond to when pop= 1, 2 or 3.