Exploring Two–Variable Data
In the context of residual plots, which of these features would indicate that a constant variance assumption might have been violated?
No obvious patterns or trends within the residual plot.
A histogram of residuals forming a normal distribution curve.
Residuals equally dispersed around both sides of zero.
The spread of residuals increasing or decreasing as fitted values increase.
If a linear regression model shows smaller residuals for data points than another model, what does this indicate about the model's fit?
The model with smaller residuals overfits the data.
The model with smaller residuals has a better fit to the data.
The size of residuals is unrelated to the model's fit.
The model with smaller residuals underestimates variability in the data.
What is NOT a relevant measurement when examining residuals in regression analysis?
Variance
Mean absolute deviation
Interquartile range
Standard deviation
Which method randomly selects individuals for a sample with no specific system or rule?
Simple random sampling
Systematic sampling
Cluster sampling
Stratified sampling
If a residual plot shows a random scatter of points around the horizontal axis, what does this indicate about the relationship between the independent and dependent variables?
There is likely a nonlinear relationship.
There is no relationship at all.
There is likely a linear relationship.
The variance of the residuals is increasing.
What might be implied if after implementing new teaching methods across various schools, we find consistently low positive residuals in standardized math test scores?
Pre-existing educational disparities among different schools have widened following these methodological shifts.
School implementations of new teaching strategies have led directly toward homogenized learning outcomes.
Students generally performed above expectations set prior to applying new teaching methods.
The previous models underestimate current trends because they do not account for recent educational changes.
What do small residuals indicate in a linear regression model?
The model is underestimating the true value by a certain amount.
The model is overestimating the true value by a certain amount.
The model is not capturing the underlying relationship in the data correctly.
The model is predicting the value of the response variable well for that point.

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What does it mean when a residual is zero?
The observed value and predicted value are the same.
The residual plot will show a distinct curve.
The independent variable has no effect on the dependent variable.
The linear regression model is perfectly accurate.
When examining a set of residual plots, which characteristic suggests homoscedasticity?
A funnel shape where residual spread decreases with higher independent variable values
Constant spread of residual values across different values of an independent variable
Clustering toward one side of the graph indicating skewness
Widening spread of residual values as independent variable values increase
If a residual plot shows a random scatter of points around the horizontal axis, what does this indicate about the model's fit to the data?
The model has constant variability.
There is a pattern suggesting non-linearity in the residuals.
The model is appropriate for the data.
The residuals are not independent of each other.