Question

If the data point is at (3, 10.5) and the prediction equation is y = -6.1x + 12.5, what is the value of the residual for this data point?

Answer 1

Given:

The data point is (3,10.5).

The prediction equation is $y=-6.1x+12.5$.

To find:

The value of the residual for this data point.

Step-by-step explanation:

The data point is (3,10.5). So, the actual value is 10.5 at $x=3$.

Prediction equation is

$y=-6.1x+12.5$

Putting $x=3$, we get

$y=-6.1(3)+12.5$

$y=-18.3+12.5$

$y=-5.8$

The formula for residual is:

Residual = Actual value - Expected value

$Residual=10.5-(-5.8)$

$Residual=10.5+5.8$

$Residual=16.3$

Therefore, the residual for the given data point is 16.3.