contour plot in multiple linear regression I have recently saw some examples about contour plots and multiple linear regression, for what I know a countour plot is obtained for having a graphical view of how the weights in a linear regression solution are related to one another. For example in the following case: !enter image description here When I substitute a value of x1=1 and x2=1 I got a value of 67 which I suppose is a point on the left grid, but why in the contour plot appears a line going from x1=2 and x2=2 (approximately) with a value of 67? A similar problem I got in the following linear regression model: !enter image description here I cannot get an intuition of from where the contour plot comes from?

You have a model $F(x_1,x_2)$ and you need to build the contour plot. So, you have , for a given level $c$, $$F(x_1,x_2)=c$$ which gives an equation of $x_2$ as a function of $x_1$.

Let us consider the first case : it writes $$50+10x_1+7x_2=c$$ so $$x_2=\frac{1}{7} (c-10 x_1-50)$$ and these are parallel straight lines.

For the second case : it writes $$50+10x_1+7x_2+5x_1x_2=c$$ so $$x_2=\frac{c-10 x_1-50}{5 x_1+7}$$ and these are hyperbolas.

For each desired value of $c$, you draw the function $x_2=\phi(x_1)$.