Question

•If the other unobserved factors are held constant, the change in ?u is then 0, ∆?=0∆u=0, then

∆?=?1∆?∆y=β_1 ∆x    

could someone please explain what this means? it is easier to see on the image not text

If the other unobserved factors are held constant, the change in u is then 0, Au - 0, thern x has a linear effect on y . β1 is therefore the slope parameter in the relationship between y and x yield-Bo Bifertilizer+u >B1measures the effect of fertilizer on yield wage = Ao + Aeduc + u → A measures the change in wage given another year of education

Answer 1

Consider a simple linear regression model as, “Yi = b0 + b1*Xi + u”, where “Yi” be the dependent variable, “X” be the independent variable and “u” be the error term shows all the other factor effecting “Yi” other than these two. Now, here “Yi” depends on “X” and “u”, => if any of these factor will change, => “Yi” will change. So, the change of “Y” is given by.

=> dYi = db0 +d(b1*X) + du, => dYi =b1*dX + du, where “b0 = constant term, => change is zero”.

Now, the above equation shows that “Yi” will change if “X” will change or ”u” will change, => other factors effecting “Y” other than “X” will change. Now, if we assume that others factors effecting “Y” other than “X” changes, => “du=0”, => the above equation can be written as, “dYi = b1*dX”, => only depends on “X”.

Now, if the model is given by, “yield = b0 + b1*fertilizer + u”, => if “du=0”, => “d(yield)” depends on “fertilizer”, => the following relation will hold.

=> d(Yield) = b1*d(fertilizer). Similarly for “wage = b0 + b1*edu + u”, => “d(wage) = b1*d(edu)”, for .