What is a residual? Explain when a residual is positive, negative, and zero.
A. A residual is the sum of the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is below the line, negative when it is above the line, and zero when the observed y-value equals the predicted y-value.
B. A residual is the sum of the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.
C. A residual is the difference between the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.
D. A residual is the difference between the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is below the line, negative when it is above the line, and zero when the observed y-value equals the predicted y-value.

C. A residual is the difference between the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.

Step-by-step explanation:

The residuals are obtained when there is some difference between the observed values and the fitted values of the data. Suppose we want to make a curve or hyperbola but the observed data does not actually give the curve required or there is some difference between the observed values and fitted values. The square of the sum of these differences is called residual.

The residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.

Residual is obtained by subtracting the predicted value from observed value.This difference called the residual is

positive when the observed value > predicted value

For a positive value the point lies above the (fitted) line.

negative when the observed value < predicted value

For a negative value the point lies below the (fitted) line.

zero when the observed value = predicted value

For a zero value the point lies on the (fitted) line.

Step-by-step explanation:

MrRoyal MrRoyal · Answer 2 · 2021-12-05T06:19:53+01:00

The true option is (c) A residual is the difference between the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.

Take for instance, we have the following data entry:

Observed value = 15

Predicted value = 14

The residual (r) would be:

[tex]\mathbf{r=15 - 14}[/tex]

[tex]\mathbf{r=1}[/tex]

A residual greater than 0 is above the line, while a residual less than 0 is below the line, and a residual of 0 is on the line.

Hence, the true statement about residuals is (c)