Question

Points and their residual values are shown in the table. Which point is farthest from the line of best fit?

Answer 1

Answer:

$(3,6.2)$

Step-by-step explanation:

Residual value the difference between the observed value of the dependent variable and the predicted value is called the residual.

Residual , $R=O-P$, where R is the residual value, O, is the observed value, and P is the predicted value. The sum and the mean of the residuals are equal to zero.

Now, we can see that the biggest magnitude of the difference is of $-1.1$ and $-1.1$ is at the point $(3,6.2)$.  ($\left | -1.1 \right |=1.1$)

Therefore, the point farthest from the line of best fit is the one whose magnitude of residual value is the most and in this case that point is $(3,6.2)$.

Answer 2

The point that is farthest from the line of best fit is the one that has the highest magnitude of residual value. In this case, that is (3, 3.6).

What is the Line of Best Fit?

The line of best fit refers to the line that goes through a scatter plot, pointing to the points that are nearest to points on the line or on both sides of the line.

To obtain the highest magnitude of difference, we need to know the Residual Value.

What is Residual Value?

Residual Value refers to the variance between the observed value of the predicted value and that of the dependent value.

Residual (R)  is given as R = O less P

From the table, it is clear that the largest Magnitude of difference is - 1.1. Again we can spot from the table that this is obtainable at the point where x = 3 and y = 6.2.

The absolute value of the Magnitude of Difference, therefore, is 1.1.

We can thus conclude that The point that is farthest from the line of best fit is the point whose residual value is the highest, that is:

The points where x = 3 and y =6.2.

Learn more about residual values at:
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