# Exercise 2

Consider the data set $(3,1), (0,1), (4,q_3)$. The corresponding regression line is given by $y=\frac{10}{13}x+{7}{13}$. Determine $q_3$.

None of the other answers are correct.

Such a $q_3$ does not exist.

$4\frac{23}{26}$

$5$

Consider the data set $(3,1), (0,1), (4,q_3)$. The corresponding regression line is given by $y=\frac{10}{13}x+{7}{13}$. Determine $q_3$.

Antwoord 1 correct
Fout
Antwoord 2 optie

Such a $q_3$ does not exist.

Antwoord 2 correct
Fout
Antwoord 3 optie

$4\frac{23}{26}$

Antwoord 3 correct
Fout
Antwoord 4 optie

$5$

Antwoord 4 correct
Correct
Antwoord 1 optie

None of the other answers are correct.

Antwoord 1 feedback

Wrong: The correct answer is among them.

Try again.

Antwoord 2 feedback

Wrong: Such a $q_3$ must exist.

Try again.

Antwoord 3 feedback

Wrong: If $w(a,b)=[1-(a\cdot 0+b)]^2$, then $w'_a(a,b)\neq -2(1-b)$.

See Partial derivatives.

Antwoord 4 feedback

Correct: \begin{align*}z(a,b)&=[ 1- (a \cdot 3 + b)]^2 + [1- (a \cdot 0 + b)]^2 +[ q_3- (a \cdot 4 + b)]^2\end{align*}

The partial derivative with respect to $a$ of $z(a,b)$ is given by
\begin{align*} z'_a(a,b)&=-6(1-3a-b)-8(q_3-4a-b)\\ & = -6-8q_3+50a+14b. \end{align*}
Hence, $z'_a(\frac{10}{13},\frac{7}{13})=-6-8q_3+50\cdot \frac{10}{13}+14 \cdot \frac{7}{13}=0$, which gives $q_3=5$.

Go on.