A data scientist is performing diagnostic checks on a linear regression model designed to predict property values. A key assumption for this type of model is homoscedasticity, which requires that the error variance in the model is constant. The data scientist needs to check for patterns in the model's residuals relative to its predicted (fitted) values. Which visualization is the most direct and standard method for assessing homoscedasticity in this context?
A histogram showing the frequency distribution of the model's residuals.
A Quartile-Quartile (Q-Q) plot of the model's residuals.
A scatter plot with the model's residuals on the y-axis and the fitted values on the x-axis.
A scatter plot matrix of the original independent and dependent variables.
The correct answer is a scatter plot of the residuals versus the fitted values. This plot is the standard diagnostic tool for checking the assumption of homoscedasticity (constant variance of errors). In a well-behaved model, the points on this plot should appear as a random cloud with no discernible pattern, indicating that the variance of the residuals is constant across all fitted values. A funnel or cone shape in the plot suggests heteroscedasticity, a violation of the assumption.
A Q-Q plot of the residuals is incorrect because it is used to assess whether the residuals follow a normal distribution, which is a different assumption of linear regression. A histogram of the residuals also serves to check for normality by displaying the distribution's shape, but it cannot reveal relationships between residuals and fitted values. A scatter plot matrix of the original variables is an exploratory data analysis tool used before modeling to examine pairwise relationships between variables, not a post-modeling diagnostic tool for assessing residual patterns.
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