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ECONOMETRICS CALCULUS.

Differentiate
with respect to

My solution:

By setting
.

(Hint: you will have to substitute b

Letting 2Σ[(y

0= Σ[(y

0= Σ(-y

0= -Σ (y

b

b

b

b

b

= (Σy

**1. The**__PRECEDING__question and solutionDifferentiate

*b*_{1}My solution:

*df(b*= 2Σ[(y_{0},b_{1})/db_{1}_{i}-b_{0}-b_{1}x_{i})*(-x_{i})]**2. the ACTUAL question**By setting

*d,f(b*= 0, show that you obtain_{0},b_{1})/d,b_{1}(Hint: you will have to substitute b

_{0}= y^{BAR}- b_{1}(x^{BAR}), and use the results from the previous question.)**3. Some properties that we can assume while answering the question.****4. The attempt at a solution**(I can't do it)Letting 2Σ[(y

_{i}-b_{0}-b_{1}x_{i})*(-x_{i})] = 00= Σ[(y

_{i}-b_{0}-b_{1}x_{i})*(-x_{i})]0= Σ(-y

_{i}x_{i})+Σb_{0}x_{i}+ Σb_{1}x_{i}^20= -Σ (y

_{i}x_{i})+b_{0}Σx_{i}+b_{1}Σx_{i}^2b

_{1}Σx_{i}^2=Σy_{i}Σx_{i}– (y^{BAR}-b_{1}x^{BAR})Σx_{i}............... (Re-arranging and substituting for b_{0})b

_{1}Σx_{i}=Σy_{i}-y^{BAR}+b_{1}x^{BAR}............................ (dividing both sides by Σx_{i})b

_{1}Σx_{i}– b_{1}xb = Σy_{i}– y^{BAR}b

_{1}(Σx_{i}– xb)=Σy_{i}– y^{BAR}b

_{1}= (Σy_{i}– yb)/(Σx_{i}– x^{BAR})= (Σy

_{i}– Σy_{i}/n)(Σx_{i}– Σx_{i}/n)
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