'Size' of intercept at linear regression I have a question about this table.

Why does the constant (intercept) change so dramatically from Model 1 to Model 2?
 A: Nick Cox provided an excellent response and I wanted to add a more intuitive answer.
Model 1
Model 1 investigates the relationship between IQ and Brain size among subjects represented by the ones in the study, regardless of those subjects' Gender, Height and Weight.
In other words, if you imagine the target population of subjects from which the subjects in the study were selected, that population includes a mixture of subjects - some may be females, some may be males, some may have a height of 5 foot 9 inches, some may have a height of 5 foot 5 inches, etc., some may have a weight 160 lbs, some may have a weight of 120 lbs, etc. Model 1 takes all of these subjects and studies the relationship between their IQ and Brain size ignoring (or not accounting for) their Gender, Height and Weight.  In other words, Model 1 mixes all of these subjects together and then studies the relationship of interest for the mixed subjects.
Model 2
Model 2 investigates the relationship between IQ and Brain size among subjects represented by the one in the study who have: the same Gender, the same Height and the same Weight.
For example, Model 2 investigates the relationship between IQ and Brain size among:

*

*males with a height of 5 foot 9 inches and a weight of 160 pounds;

*females with a height of 5 foot 5 inches and a weight of 120 pounds, etc.

Model 2 makes the assumption that the relationship betwewn IQ and Brain size is the same for all of these population subsets defined by combinations of values of Gender, Height and Weight supported by the ones present in your data. This relationship is called an adjusted relationship, since it is adjusted for of Gender, Height and Weight.  In contrast, the relationship betwewn IQ and Brain size investigated via Model 1 is an unadjusted relationship.
Model 2 is selective about which subjects it considers - rather than mixing all subjects together, it focuses on subsets of subjects in the target population sharing the same Gender, the same Height and the same Weight.
Intercept Interpretation in Model 1
For Model 1, the (true) intercept represents the average value of IQ in the target population for those subjects for whom Brain size is equal to 0. Clearly, such subjects do not exist - if they did, they would be brainless.
Intercept Interpretation in Model 2
For Model 2, the (true) intercept represents the average value of IQ in the target population for those subjects for whom Brain size is equal to 0, Gender is equal to male, Height is equal to 0 inches and Weight is equal to 0 lbs. Again, such subjects do not exist.
Neither of the two intercepts has a realistic interpretation. If you mean-center the variable Brain size in Model 1 and the variables Brain size, Height and Weight in Model 2, you will get intercepts with a more realistic interpretation from the refitted models. Note, however, that slope coefficients in the two regression models you have here are interpretable even if the intercept has no meaningful interpretation in practice.
Intercept Interpretation in Model 1 after Mean-Centering Brain size
For the revised Model 1, the (true) intercept represents the average value of IQ in the target population for those subjects with an average Brain size.
Intercept Interpretation in Model 2 after Mean-Centering Brain size, Height and Weight
For the revised Model 2, the (true) intercept represents the average value of IQ in the target population for male subjects with an average Brain size, average Height and average Weight.
A: The coefficients of each predictor are almost always going to change when you add more predictors. This is an example of the answer changing when you ask a different question.
Your software should let you fit a regression with no predictor at all. For example, if I try to predict people's weights with a regression with no predictors, then I will get the mean weight as a prediction. That will be shown as the intercept or constant.
If I then add height as a predictor, the intercept $b_0$ in
predicted weight $= b_0 + b_1$ height
is the prediction for a hypothetical someone with zero height. (Imagine plugging in height $= 0$; then the term with coefficient $b_1$ vanishes.) The intercept reported for $b_0$ in this case  is going to be way outside the data and may even be returned as a negative number.
If I add an indicator say 1 if male and 0 if female, so that the model now is
predicted weight $= b_0 + b_1$ height $+\ b_2$ male
the intercept is now the prediction for a hypothetical someone with zero height and who is female (for whom male $= 0$). That will be different again, but not so much.
In general in
$\hat y = b_0 + b_1 x_1 + \cdots + b_J x_J = b_0 + \sum_{j=1}^J x_j$
the intercept $b_0$ is what is predicted when all the $x_j$ (so all $x_1$ to $x_J$) are zero. The intercept may be, in practice, an implausible or impossible value but that makes no difference to the principle. So, as the set of $x_j$s changes, so also will the intercept.
