The gradient of our cost function includes a sum over contributions of individual points. We could calculate the individual contributions separately.

The gradient for a single

$($

x

$($

i

$)$

$,$

y

$($

i

$)$

$)$

$($x

$($i$)$

$,$y

$($i$)$

$)$ point is:

$[$

$($

w

$0$

$+$

w

$1$

$$

x

$1$

$($

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$$

y

$($

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$)$

$($

w

$0$

$+$

w

$1$

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x

$1$

$($

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$$

y

$($

i

$)$

$)$

x

$1$

$($

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$)$

$]$

$[$

$($w

$0$

$$

$+$w

$1$

$$

$$x

$1$

$($i$)$

$$

$$y

$($i$)$

$)$

$($w

$0$

$$

$+$w

$1$

$$

$$x

$1$

$($i$)$

$$

$$y

$($i$)$

$)$x

$1$

$($i$)$

$$

$$

$]$

For the line

y

$=$

$2$

x

$1$

y$=2$x

$1$

$$

$,$ what is the gradient contribution for each of the four examples?