Let's say we want to predict weight ($y$) of a person based on age ($x_1$) using linear regression.
Assume a simple linear regression
$y = m*x_1 + c_1 $
Now we want to include height ($x_2$) of a person in the model. So we have a multiple linear regression
$y = m_1 * x_1 + m_2 * x_2 + c_2 $
I am wondering how we can interpret the relationship between m and $m_1$. Considering we have same dependent variable and one of the independent variables is same, can we compare $m$ and $m_1$?
If we can,
2.1 when $m_1$ < $m$, would saying "controlling for $x_2$ decreases the effect of $x_1$" be accurate?
2.2 when $m_1$ > $m$, would saying "controlling $x_2$ increases the effect of $x_1$" be accurate?
For simplicity, we can assume all regression coefficients are positive, i.e. $m$, $m_1$, $m_2$ $> 0$.