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MLS-C01 · Question #106

A Machine Learning Specialist is attempting to build a linear regression model. Given the displayed residual plot only, what is the MOST likely problem with the model?

The correct answer is A. Linear regression is inappropriate. The residuals do not have constant variance. The provided residual plot for a linear regression model shows a non-random pattern with varying variance across predicted values.

Modeling

Question

A Machine Learning Specialist is attempting to build a linear regression model. Given the displayed residual plot only, what is the MOST likely problem with the model?

Exhibit

MLS-C01 question #106 exhibit

Options

  • ALinear regression is inappropriate. The residuals do not have constant variance.
  • BLinear regression is inappropriate. The underlying data has outliers.
  • CLinear regression is appropriate. The residuals have a zero mean.
  • DLinear regression is appropriate. The residuals have constant variance.

How the community answered

(55 responses)
  • A
    78% (43)
  • B
    7% (4)
  • C
    4% (2)
  • D
    11% (6)

Why each option

The provided residual plot for a linear regression model shows a non-random pattern with varying variance across predicted values.

ALinear regression is inappropriate. The residuals do not have constant variance.Correct

A key assumption of linear regression is homoscedasticity, meaning the variance of the residuals should be constant across all levels of the independent variable. If a residual plot shows a fanning-out or fanning-in pattern, it indicates heteroscedasticity (non-constant variance), which implies that linear regression might be an inappropriate model without transformation or a different modeling approach.

BLinear regression is inappropriate. The underlying data has outliers.

While outliers can be observed in residual plots, the most evident problem when variance changes with predicted values is heteroscedasticity, a fundamental violation of linear regression assumptions.

CLinear regression is appropriate. The residuals have a zero mean.

While a zero mean for residuals is generally desirable, the primary issue depicted by a non-constant spread in a residual plot is the violation of the constant variance assumption, not solely the mean.

DLinear regression is appropriate. The residuals have constant variance.

The residual plot explicitly demonstrates that the residuals do not have constant variance, making this statement incorrect.

Concept tested: Interpreting residual plots for homoscedasticity

Source: https://en.wikipedia.org/wiki/Homoscedasticity_and_heteroscedasticity

Topics

#Linear Regression#Residual Analysis#Model Diagnostics#Heteroscedasticity

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