Chapter 4.5, Problem 2E

To determine

To explain: Theway to use residuals to determine the degree of accuracy to which a line of fit models a data set.

Answer to Problem 2E

  $\mathrm{Residual}=\left(y-valueofgivendatacoordinate\right)-\left(y-valuederivedfrommodel\right)$ .

Further explanation is given below.

Explanation of Solution

Given information: The way to use residuals to check accuracy of a model is to be elaborated.

  $\mathrm{Residual}=\left(y-valueofgivendatacoordinate\right)-\left(y-valuederivedfrommodel\right)$

Considering the above stated formula, several interpretations can be comprehended,

First of all find all the residuals and make a scatter plot out of them,

If all coordinates are evenly hovering extremely close to the both sides of horizontal axis,then the line of fit quite accurately models a dataset. If the residual coordinates are forming a pattern then there must be a considerable discrepancy and line of fit doesn’t quite accurately model the data values. Grossly scattered residual coordinates imply that there is no correlation between the components (see formula) of residuals and line of fit doesn’t accurately models the data values.