Question

Analyze the residual plot below and identify which, if any, of the conditions for an adequate linear model is not met.

A residual plot has a horizontal axis labeled Explanatory from less than 5 to 25 plus in increments of 10 and a vertical axis labeled residuals from less than negative negative 2 to negative 2 plus in increments of 1. A horizontal dashed line intersects the vertical axis at 0. A series of plotted points is generally between horizontal coordinates 5 and 25 and between vertical coordinates negative 2 and 2. There are two plotted points at left parenthesis 17 comma 3.9 right parenthesis and left parenthesis 19 comma 4 right parenthesis. All coordinates are approximate.

Which of the conditions below might indicate that a linear model would not beΓÇï appropriate?

a. None
b. Patterned residuals
c. Constant error variance
d. Outlier

Answer 1

The provided residual plot indicates that there is an outlier (d), which is a condition that suggests a linear model may not be appropriate. The residuals for two points exceed the acceptable range and can significantly affect the best-fit line, leading to an inaccurate model.

Step-by-step explanation:

To analyze the residual plot described, we note that residuals are the difference between observed values and the values predicted by a linear model. An ideal residual plot, when the linear model is appropriate, will show residuals scattered randomly around the horizontal axis (where the residual value is zero) without forming any discernible pattern, exhibiting constant error variance, and not having any outliers.

According to the provided residual plot information, most of the plotted points are within the acceptable range, between -2 and 2. However, two points are mentioned with coordinates (17, 3.9) and (19, 4), which are clearly outliers since their residual values are higher than the given threshold. A single outlier in a dataset can significantly affect the best-fit line, potentially skewing the slope and intercept of the line, and thus making our model inaccurate. The presence of outliers suggests that the linear model may be inadequate for the data set because it violates the condition that there should be no outliers.Considering this, the answer to the question is d. Outlier. The condition for an adequate linear model that is not met is that there should be no outliers, given that all residuals should ideally fall within the range of -2 to 2 for the standard deviation considered.