Question

Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data.

a)x-valuesResiduals
A scatterplot with horizontal axis labeled "x-values" and vertical axis labeled "Residuals" contains points that appear randomly distributed.
b)x-valuesResiduals
A scatterplot with horizontal axis labeled "x-values" and vertical axis labeled "Residuals" contains points whose general pattern is a curve that falls and then rises from left to right.
c)x-valuesResiduals
A scatterplot with horizontal axis labeled "x-values" and vertical axis labeled "Residuals" contains points that have a wide vertical range on the left side of the plot and which become more and more tightly clustered from left to right. Points on the right side of the graph tightly follow the path of a horizontal line.
Question content area bottom
(a) Choose the best answer for residuals plot (a).
A The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases
as the values of the explanatory variable increases.
OB. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power increases
as the values of the explanatory variable increases.
Oc. The scattered residuals plot indicates an appropriate linear model.
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(b) Choose the best answer for residuals plot (b).
OA. The scattered residuals plot indicates an appropriate linear model.
OB. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship
is not linear.
Oc. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases
as the values of the explanatory variable increases.

Answer 1

(a) The best answer for residuals plot (a) is:

A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

A fanned pattern in the residuals plot suggests that the linear model is not appropriate because the variability of the residuals increases as the values of the explanatory variable increases. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

(b) The best answer for residuals plot (b) is:

B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear.

A curved pattern in the residuals plot suggests that the linear model is not appropriate because the relationship between the variables is not linear. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.