Residual Plots Analysis
Analyze residual plots to determine the appropriateness of linear models and identify patterns in data.
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Residual Plots Analysis
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Carefully analyze each residual plot to determine if a linear model is appropriate for the data. Explain your reasoning for each question.
1. What does a residual represent in a regression analysis?
The difference between the predicted and observed value.
The slope of the regression line.
The y-intercept of the regression line.
The correlation coefficient.
2. A good residual plot should ideally show:
A clear pattern, such as a curve.
Random scattering of points around zero.
A funnel shape.
An increasing or decreasing trend.
3. Consider a residual plot where the points form a distinct 'U' shape. What does this suggest about the appropriateness of a linear model for the original data?
4. If a residual plot shows increasing spread (a 'fan' or 'funnel' shape) as the predicted values increase, what assumption of linear regression is likely violated?
5. Examine the residual plot below. Is a linear model appropriate for the data? Explain your reasoning.
6. Examine the residual plot below. Is a linear model appropriate for the data? Explain your reasoning.
7. If a residual plot shows a clear upward trend, it indicates that the linear model is a good fit.
True
False
8. Heteroscedasticity in a residual plot suggests that the variance of the residuals is constant across all predicted values.
True
False
9. A residual plot that shows a random scatter of points around the horizontal line at zero suggests that a is appropriate.
10. When a residual plot exhibits a curved pattern, it indicates that a relationship might be more suitable for the data.
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