The correct option is C.
Yes, the residuals do not display constant error variance.
Analyzing a residual plot is a key part of regression analysis as it helps to validate the fit of a model. The residuals are the differences between the observed values and the values predicted by the model. For an adequate linear model, we typically look for three things in a residual plot:
1. The residuals should be randomly dispersed around the horizontal axis (indicating that the model's predictions are unbiased).
2. There should be no discernible pattern in the residuals (which would suggest that the model is missing a relationship and is perhaps not the best fit).
3. The residuals should have constant variance (homoscedasticity), meaning that the spread of the residuals should be roughly the same across all values of the independent variable(s).
From the provided image, we need to determine if the residual plot shows any of these violations:
- If the residuals seem to be randomly scattered without any clear pattern, the answer would be A: "No; the plot of residuals is random."
- If there is a discernible pattern or systematic structure to the residuals, the answer would be B: "Yes; there is a discernible pattern in the residuals."
- If the spread of residuals appears to be different across the range of values (e.g., if they fan out or in as we move along the x-axis), then the answer would be C: "Yes; the residuals do not display constant error variance."