Wooldrige says that ‘intuitively, to estimate k+1 parameters, we need at least k+1 observations’. Why is this the case?
The intuition is that OLS is a linear model and to estimate any linear model you need at least 2 points in 2D space. The reason for that is that with a single point you can’t uniquely identify any line.
Adding extra parameter increases the dimensions and in each higher dimension you need one more point to estimate linear model. You can think about it in a way that you need at least one point per dimension but in 1D space there is no line since 1D would be just Y axis hence you get minimum k+1 points.