Question

If the residual positive, what does that mean and how does it compare with the line of best fit? What about if the residual is negative?

a) What does it mean if the residual is close to 0? What if the residual isn't close to 0?

b) How would each of these residuals appear in a scatter plot?

Answer 1

(1)

(i) The Residual is the observed value minus predicted value.

If the Residual is positive, it means that the observed value is greater than the predicted value. Above the Line of Best Fit, we under - predicted, so we have a positive residual.

(ii)

If the Residual is negative, it means that the observed value is less than the predicted value. Below the Line of Best Fit, we over - predicted, so we have a negative residual.

(a)

It residual is close to 0, it indicates that the prediction is exactly correct.

If the residual is not close to 0, it indicated that the prediction is not correct.

(b)
In the scatter plot:

Appropriate Linear Model: When the plots are randomly placed, above and belowx - axis

AppropriateNon-linearModel: When plots follow a pattern, resembling a curve.