The answer is no. You were learning the coefficient independently without considering the 4 features together.

Let me use a simple example to explain.

Assume the real regression result is: $10*x_1 -1*x_2 = y$

Assume in your samples $x_1, x_2$ have a positive relationship with $y$. Meaning when $x$ increases $y$ increases too. This is not too hard to do by choosing the samples, e.g.

1, 2 -> 8,
2, 3 -> 17,
3, 4 -> 26
...

Learning coefficient of $x_1, x_2$ separately will always give positive coefficients $a$.

Never will it learn $-1$.

The answer is no. You were learning the coefficient independently without considering the 4 features together.

Let me use a simple example to explain.

Assume the real regression result is: $10*x_1 -1*x_2 = y$

Assume in your samples $x_1, x_2$ have a positive relationship with $y$. Meaning when $x$ increases $y$ increases too. This is not too hard to do by choosing the samples, e.g.

1, 2 -> 8,
2, 3 -> 17,
3, 4 -> 26
...

Learning coefficient of $x_1, x_2$ separately will always give positive coefficients $a_1, a_2$.

Never will it learn $-1$.

The answer is no. You were learning the coefficient independently without considering the 4 features together.

Let me use a simple example without residual $b$ to explain.

Assume the real regression result is $x_1 -2x_2 = y$

Assume in your samples $x_1, x_2, y$ are all positive

Learning coefficient of $x_1, x_2$ separately will always give positive coefficients $a$.

Never will it learn $-2$.

The answer is no. You were learning the coefficient independently without considering the 4 features together.

Let me use a simple example to explain.

Assume the real regression result is: $10*x_1 -1*x_2 = y$

Assume in your samples $x_1, x_2$ have a positive relationship with $y$. Meaning when $x$ increases $y$ increases too. This is not too hard to do by choosing the samples, e.g.

1, 2 -> 8,
2, 3 -> 17,
3, 4 -> 26
...

Learning coefficient of $x_1, x_2$ separately will always give positive coefficients $a$.

Never will it learn $-1$.