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 $q_3$.
Such a $q_3$ does not exist.
$4\frac{23}{26}$
$5$
None of the other answers are correct.
Wrong: The correct answer is among them.
Try again.
Wrong: Such a $q_3$ must exist.
Try again.
Wrong: If $w(a,b)=[1-(a\cdot 0+b)]^2$, then $w'_a(a,b)\neq -2(1-b)$.
See Partial derivatives.
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.