Evaluate Model Fit with Residuals - Statistics
Card 1 of 30
Identify the better fit if Model A residuals are mostly within $\pm 1$ and Model B within $\pm 5$.
Identify the better fit if Model A residuals are mostly within $\pm 1$ and Model B within $\pm 5$.
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Model A. Smaller residuals indicate better fit.
Model A. Smaller residuals indicate better fit.
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Identify the better fit if residuals for Model 1 show random scatter and Model 2 show a U-shape.
Identify the better fit if residuals for Model 1 show random scatter and Model 2 show a U-shape.
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Model 1. Random pattern beats systematic pattern.
Model 1. Random pattern beats systematic pattern.
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What is the predicted value $\hat{y}$ if $y=25$ and the residual is $-3$?
What is the predicted value $\hat{y}$ if $y=25$ and the residual is $-3$?
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$28$. Since $y-\hat{y}=-3$, then $\hat{y}=y+3=25+3=28$.
$28$. Since $y-\hat{y}=-3$, then $\hat{y}=y+3=25+3=28$.
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Which residual-plot pattern indicates a good fit: random scatter around $0$ or a clear curve?
Which residual-plot pattern indicates a good fit: random scatter around $0$ or a clear curve?
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Random scatter around $0$. No pattern in residuals indicates the model fits well.
Random scatter around $0$. No pattern in residuals indicates the model fits well.
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Identify the conclusion if residuals show a curved pattern around $0$ as $x$ increases.
Identify the conclusion if residuals show a curved pattern around $0$ as $x$ increases.
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The model form is wrong; a nonlinear model may fit better. Curved residual pattern suggests linear model is inappropriate.
The model form is wrong; a nonlinear model may fit better. Curved residual pattern suggests linear model is inappropriate.
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Identify the issue if residuals fan out (spread increases) as $x$ increases.
Identify the issue if residuals fan out (spread increases) as $x$ increases.
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Non-constant variance (heteroscedasticity). Increasing spread violates constant variance assumption.
Non-constant variance (heteroscedasticity). Increasing spread violates constant variance assumption.
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Identify the issue if residuals fan in (spread decreases) as $x$ increases.
Identify the issue if residuals fan in (spread decreases) as $x$ increases.
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Non-constant variance (heteroscedasticity). Decreasing spread violates constant variance assumption.
Non-constant variance (heteroscedasticity). Decreasing spread violates constant variance assumption.
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What does a residual plot with points clustered far from $0$ suggest about the model?
What does a residual plot with points clustered far from $0$ suggest about the model?
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Large typical errors; the fit is poor. Large residuals indicate poor predictions overall.
Large typical errors; the fit is poor. Large residuals indicate poor predictions overall.
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What is the residual for $y=18$ when the model predicts $\hat{y}=20$?
What is the residual for $y=18$ when the model predicts $\hat{y}=20$?
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$-2$. Calculate $18-20=-2$.
$-2$. Calculate $18-20=-2$.
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What is the residual for $y=42$ when the model predicts $\hat{y}=39$?
What is the residual for $y=42$ when the model predicts $\hat{y}=39$?
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$3$. Calculate $42-39=3$.
$3$. Calculate $42-39=3$.
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Identify whether the model overpredicts or underpredicts when the residual is $-5$.
Identify whether the model overpredicts or underpredicts when the residual is $-5$.
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Overpredicts. Negative residual means $\hat{y}>y$.
Overpredicts. Negative residual means $\hat{y}>y$.
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Identify whether the model overpredicts or underpredicts when the residual is $+7$.
Identify whether the model overpredicts or underpredicts when the residual is $+7$.
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Underpredicts. Positive residual means $y>\hat{y}$.
Underpredicts. Positive residual means $y>\hat{y}$.
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What does a residual plot with many points exactly on $0$ indicate about predictions?
What does a residual plot with many points exactly on $0$ indicate about predictions?
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Many data points are predicted exactly by the model. Zero residuals mean perfect predictions for those points.
Many data points are predicted exactly by the model. Zero residuals mean perfect predictions for those points.
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What is the residual for a data point with observed $y$ and predicted value $\hat{y}$?
What is the residual for a data point with observed $y$ and predicted value $\hat{y}$?
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$y-\hat{y}$. Residual measures the vertical distance from observed to predicted.
$y-\hat{y}$. Residual measures the vertical distance from observed to predicted.
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What does a positive residual $y-\hat{y}>0$ mean about the model prediction?
What does a positive residual $y-\hat{y}>0$ mean about the model prediction?
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The model underpredicts the actual $y$ value. Positive residual means observed exceeds predicted.
The model underpredicts the actual $y$ value. Positive residual means observed exceeds predicted.
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What does a negative residual $y-\hat{y}<0$ mean about the model prediction?
What does a negative residual $y-\hat{y}<0$ mean about the model prediction?
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The model overpredicts the actual $y$ value. Negative residual means predicted exceeds observed.
The model overpredicts the actual $y$ value. Negative residual means predicted exceeds observed.
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Which plot is used to assess model fit by graphing residuals versus the explanatory variable $x$?
Which plot is used to assess model fit by graphing residuals versus the explanatory variable $x$?
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A residual plot (residuals vs. $x$). Plots residuals on y-axis against x-values to reveal patterns.
A residual plot (residuals vs. $x$). Plots residuals on y-axis against x-values to reveal patterns.
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Choose the correct residual: observed $y=10$, predicted $\hat{y}=6$; is it $4$ or $-4$?
Choose the correct residual: observed $y=10$, predicted $\hat{y}=6$; is it $4$ or $-4$?
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$4$. Calculate $10-6=4$.
$4$. Calculate $10-6=4$.
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Choose the correct residual: observed $y=6$, predicted $\hat{y}=10$; is it $4$ or $-4$?
Choose the correct residual: observed $y=6$, predicted $\hat{y}=10$; is it $4$ or $-4$?
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$-4$. Calculate $6-10=-4$.
$-4$. Calculate $6-10=-4$.
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What is the observed value $y$ if $\hat{y}=50$ and the residual is $6$?
What is the observed value $y$ if $\hat{y}=50$ and the residual is $6$?
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$56$. Since $y-\hat{y}=6$, then $y=\hat{y}+6=50+6=56$.
$56$. Since $y-\hat{y}=6$, then $y=\hat{y}+6=50+6=56$.
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Identify the model issue if residual spread increases as $x$ increases (a widening band).
Identify the model issue if residual spread increases as $x$ increases (a widening band).
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Nonconstant variance (heteroscedasticity). Variance should be constant; increasing spread violates this.
Nonconstant variance (heteroscedasticity). Variance should be constant; increasing spread violates this.
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Identify the model issue if residuals are positive for small $x$ and negative for large $x$ in a smooth trend.
Identify the model issue if residuals are positive for small $x$ and negative for large $x$ in a smooth trend.
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Nonlinear pattern; the model form is wrong. Systematic sign changes suggest a linear model misses curvature.
Nonlinear pattern; the model form is wrong. Systematic sign changes suggest a linear model misses curvature.
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Which option best indicates a good fit: residuals centered at $0$ or centered far from $0$?
Which option best indicates a good fit: residuals centered at $0$ or centered far from $0$?
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Centered at $0$. Residuals balanced around zero indicate unbiased predictions.
Centered at $0$. Residuals balanced around zero indicate unbiased predictions.
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Which option indicates the model tends to underpredict: residuals mostly $>0$ or mostly $<0$?
Which option indicates the model tends to underpredict: residuals mostly $>0$ or mostly $<0$?
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Mostly $>0$. Positive residuals mean observed values exceed predictions.
Mostly $>0$. Positive residuals mean observed values exceed predictions.
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Identify the residual if $y=7$ and $\hat{y}=10$.
Identify the residual if $y=7$ and $\hat{y}=10$.
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$-3$. Calculate $7-10=-3$ since residual equals observed minus predicted.
$-3$. Calculate $7-10=-3$ since residual equals observed minus predicted.
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Identify the residual if $y=12$ and $\hat{y}=9$.
Identify the residual if $y=12$ and $\hat{y}=9$.
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$3$. Calculate $12-9=3$ since residual equals observed minus predicted.
$3$. Calculate $12-9=3$ since residual equals observed minus predicted.
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What is the reference line drawn on a residual plot to judge model fit?
What is the reference line drawn on a residual plot to judge model fit?
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The horizontal line $y=0$. Zero line helps identify if residuals are balanced above and below.
The horizontal line $y=0$. Zero line helps identify if residuals are balanced above and below.
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Which residual plot feature indicates possible outliers in the $y$-direction?
Which residual plot feature indicates possible outliers in the $y$-direction?
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One or more unusually large $|y-\hat{y}|$ values. Points far from zero line have large prediction errors.
One or more unusually large $|y-\hat{y}|$ values. Points far from zero line have large prediction errors.
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Which residual plot pattern suggests nonconstant variance (heteroscedasticity)?
Which residual plot pattern suggests nonconstant variance (heteroscedasticity)?
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A fan or funnel shape in residual spread. Changing spread violates the constant variance assumption.
A fan or funnel shape in residual spread. Changing spread violates the constant variance assumption.
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Which residual plot pattern suggests nonlinearity (a curved relationship) in the data?
Which residual plot pattern suggests nonlinearity (a curved relationship) in the data?
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A systematic curve (U-shape or S-shape). Curved patterns in residuals indicate the relationship isn't linear.
A systematic curve (U-shape or S-shape). Curved patterns in residuals indicate the relationship isn't linear.
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