Question

Given the line of the best fit for a set of data points with equation y=-5x-2.5 what is the residual for the point (3,6)

Apex

Answer 1

The residual of the point
`(3,6)` in the equation
`y=-5(x)-2.5` is
`= 23.5`

Explanation:

We have been given point
`(3,6)` where
`x=3`.

Now the equation is
`y=-5(x)-2.5`.

Plugging the value of
`x=3` in the equation of
`y=-5(x)-2.5`,

we have to find the predicted value of y and
`y=-5(3)-2.5 =-15-2.5=-17.5`.

So y predicted
`=-17.5`.

To find the residual point we have to subtract the actual value from the predicted value.

As actual value of
`y=6` along with the points
`(3,6)`.

Residual point = Actual value - Predicted value.

`=6 -(-17.5) =23.5`

So the residual for the point
`(3,6)` is
`23.5`.