ECONOMETRICS CALCULUS.(adsbygoogle = window.adsbygoogle || []).push({});

1. The PRECEDING question and solution

Differentiate with respect tob_{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 settingd,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})] = 0

0= 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}^2

0= -Σ (y_{i}x_{i})+b_{0}Σx_{i}+b_{1}Σx_{i}^2

b_{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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# Homework Help: Ridiculous manipulation question

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