AP Statistics Flashcards: Residuals

What this deck covers

This deck focuses on Residuals, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is it called when residuals do not have constant variance?

Answer: Heteroscedasticity. This indicates unequal variance across different prediction levels.

Flashcard 2: What is the implication of heteroscedasticity in residuals?

Answer: Model may need transformation. Unequal variance violates regression assumptions.

Flashcard 3: Identify the condition if residuals form a funnel shape.

Answer: Heteroscedasticity. The funnel pattern shows non-constant variance.

Flashcard 4: What is indicated by residuals tightly clustering around zero?

Answer: Good model fit. Small residuals near zero indicate accurate predictions.

Flashcard 5: How does one interpret a residual value of zero?

Answer: Observed equals predicted value. Perfect prediction with no error at that point.

Flashcard 6: Find the residual if $y = 7$ and $\hat{y} = 7$.

Answer: Residual = 0. Using the formula: $7 - 7 = 0$.

Flashcard 7: What does a residual plot with no discernible pattern indicate?

Answer: A good fit for the regression model. Random scatter indicates the model captures the relationship well.

Flashcard 8: What is it called when residuals do not have constant variance?

Answer: Heteroscedasticity. This indicates unequal variance across different prediction levels.

Flashcard 9: What does the presence of outliers in residuals suggest?

Answer: Potential leverage points or anomalies. Outliers may indicate unusual data points or model problems.

Flashcard 10: State the formula for calculating a residual.

Answer: Residual = Observed value - Predicted value. This formula shows the error between actual and predicted values.

Flashcard 11: What does a residual of zero imply about the fit at that point?

Answer: Perfect fit for that observed value. The prediction exactly matches the observed value.

Flashcard 12: What is a residual in the context of regression analysis?

Answer: A residual is the difference between an observed value and its predicted value. This measures how far each data point is from the regression line.

Flashcard 13: What is the residual for observed $y = 14$ and predicted $\hat{y} = 9$?

Answer: Residual = 5. Using the formula: $14 - 9 = 5$.

Flashcard 14: Find the residual for observed $y = 21$ and predicted $\hat{y} = 19$.

Answer: Residual = 2. Using the formula: $21 - 19 = 2$.

Flashcard 15: What is the result when residuals are analyzed in a good model?

Answer: Random scatter around zero. Random scatter indicates no systematic prediction errors.

Flashcard 16: What is a common graphical tool to evaluate the fit of a regression model?

Answer: Residual plot. This graph reveals model assumptions and fit quality.

Flashcard 17: What does a residual plot help to identify in a regression model?

Answer: Patterns indicating model inadequacy. Non-random patterns suggest the model needs improvement.

Flashcard 18: What does a large residual indicate about the model's prediction?

Answer: Poor prediction accuracy. Large residuals show the model made significant prediction errors.

Flashcard 19: What does a residual plot help to identify in a regression model?

Answer: Patterns indicating model inadequacy. Non-random patterns suggest the model needs improvement.

Flashcard 20: What does a negative residual indicate about the observed value?

Answer: Observed value is less than predicted value. The model overestimated the actual value.

Flashcard 21: What is the residual for $y = 13$ and $\hat{y} = 16$?

Answer: Residual = -3. Using the formula: $13 - 16 = -3$.

Flashcard 22: Find the residual for observed $y = 15$ and predicted $\hat{y} = 18$.

Answer: Residual = -3. Using the formula: $15 - 18 = -3$.

Flashcard 23: What is the residual for observed $y = 14$ and predicted $\hat{y} = 9$?

Answer: Residual = 5. Using the formula: $14 - 9 = 5$.

Flashcard 24: Which plot is used to detect non-linearity in a model?

Answer: Residual plot. Curved patterns in residuals reveal non-linear relationships.

Flashcard 25: Which term describes residuals that display constant spread?

Answer: Homoscedasticity. Equal spread indicates the regression assumptions are met.

Flashcard 26: State the formula for calculating a residual.

Answer: Residual = Observed value - Predicted value. This formula shows the error between actual and predicted values.

Flashcard 27: What does a pattern in a residual plot suggest about a model?

Answer: The model may be inadequate or misspecified. Patterns suggest the linear model doesn't fit the data properly.

Flashcard 28: Find the residual for $y = 11$ and $\hat{y} = 14$.

Answer: Residual = -3. Using the formula: $11 - 14 = -3$.

Flashcard 29: What does a systematic pattern in residuals indicate?

Answer: Model inadequacy or bias. Systematic patterns reveal the model doesn't capture all relationships.

Flashcard 30: Identify the term for a plot of residuals versus predicted values.

Answer: Residual plot. This graph shows residuals on y-axis and predicted values on x-axis.

Flashcard 31: Identify the term for a plot of residuals versus predicted values.

Answer: Residual plot. This graph shows residuals on y-axis and predicted values on x-axis.

Flashcard 32: What is the sum of residuals in a least squares regression?

Answer: Zero. This is a property of least squares regression.

Flashcard 33: Explain the implication of a residual plot showing a pattern.

Answer: Model may be misspecified or missing variables. Patterns indicate the linear model is not appropriate.

Flashcard 34: What is the implication of heteroscedasticity in residuals?

Answer: Model may need transformation. Unequal variance violates regression assumptions.

Flashcard 35: What does a residual of zero imply about the fit at that point?

Answer: Perfect fit for that observed value. The prediction exactly matches the observed value.

Flashcard 36: Find the residual for $y = 5$ and $\hat{y} = 9$.

Answer: Residual = -4. Using the formula: $5 - 9 = -4$.

Flashcard 37: Find the residual with $y = 8$ and $\hat{y} = 10$.

Answer: Residual = -2. Using the formula: $8 - 10 = -2$.

Flashcard 38: Find the residual for $y = 11$ and $\hat{y} = 14$.

Answer: Residual = -3. Using the formula: $11 - 14 = -3$.

Flashcard 39: What is the sum of residuals in a least squares regression?

Answer: Zero. This is a property of least squares regression.

Flashcard 40: Find the residual for observed value $y = 10$ and predicted value $\hat{y} = 8$.

Answer: Residual = 2. Using the formula: $10 - 8 = 2$.

Flashcard 41: What is the residual for $y = 12$ and $\hat{y} = 13$?

Answer: Residual = -1. Using the formula: $12 - 13 = -1$.

Flashcard 42: Which term describes residuals having constant variance?

Answer: Homoscedasticity. This means residuals have equal spread across all predicted values.

Flashcard 43: Find the residual for $y = 5$ and $\hat{y} = 9$.

Answer: Residual = -4. Using the formula: $5 - 9 = -4$.

Flashcard 44: What does a positive residual indicate about the observed value?

Answer: Observed value is greater than predicted value. The model underestimated the actual value.

Flashcard 45: Which condition is violated if residuals display a cone shape?

Answer: Constant variance (homoscedasticity). A cone shape shows variance increases or decreases with predicted values.

Flashcard 46: Which condition is violated if residuals display a cone shape?

Answer: Constant variance (homoscedasticity). A cone shape shows variance increases or decreases with predicted values.

Flashcard 47: Find the residual with $y = 8$ and $\hat{y} = 10$.

Answer: Residual = -2. Using the formula: $8 - 10 = -2$.

Flashcard 48: Which statistical measure do residuals help to check?

Answer: Model adequacy. Residuals help determine if the model fits the data well.

Flashcard 49: Find the residual for $y = 17$ and $\hat{y} = 15$.

Answer: Residual = 2. Using the formula: $17 - 15 = 2$.

Flashcard 50: What is the purpose of analyzing residuals in regression?

Answer: To assess the fit of a regression model. Residuals reveal how well the model predicts actual values.

Flashcard 51: What does a negative residual indicate about the observed value?

Answer: Observed value is less than predicted value. The model overestimated the actual value.

Flashcard 52: Which term describes residuals having constant variance?

Answer: Homoscedasticity. This means residuals have equal spread across all predicted values.

Flashcard 53: Which statistical measure do residuals help to check?

Answer: Model adequacy. Residuals help determine if the model fits the data well.

Flashcard 54: Identify the term for the graphical representation of residuals.

Answer: Residual plot. This visual tool helps identify patterns in model errors.

Flashcard 55: Identify the condition if residuals form a funnel shape.

Answer: Heteroscedasticity. The funnel pattern shows non-constant variance.

Flashcard 56: What is the result when residuals are analyzed in a good model?

Answer: Random scatter around zero. Random scatter indicates no systematic prediction errors.

Flashcard 57: Explain the implication of a residual plot showing a pattern.

Answer: Model may be misspecified or missing variables. Patterns indicate the linear model is not appropriate.

Flashcard 58: Find the residual for observed value $y = 10$ and predicted value $\hat{y} = 8$.

Answer: Residual = 2. Using the formula: $10 - 8 = 2$.

Flashcard 59: What does the presence of outliers in residuals suggest?

Answer: Potential leverage points or anomalies. Outliers may indicate unusual data points or model problems.

Flashcard 60: What is a common graphical tool to evaluate the fit of a regression model?

Answer: Residual plot. This graph reveals model assumptions and fit quality.

Flashcard 61: What is the purpose of analyzing residuals in regression?

Answer: To assess the fit of a regression model. Residuals reveal how well the model predicts actual values.

Flashcard 62: What is a residual in the context of regression analysis?

Answer: A residual is the difference between an observed value and its predicted value. This measures how far each data point is from the regression line.

Flashcard 63: What does a systematic pattern in residuals indicate?

Answer: Model inadequacy or bias. Systematic patterns reveal the model doesn't capture all relationships.

Flashcard 64: What is the residual for $y = 12$ and $\hat{y} = 13$?

Answer: Residual = -1. Using the formula: $12 - 13 = -1$.

Flashcard 65: Identify the term for the graphical representation of residuals.

Answer: Residual plot. This visual tool helps identify patterns in model errors.

Flashcard 66: What is the residual for $y = 13$ and $\hat{y} = 16$?

Answer: Residual = -3. Using the formula: $13 - 16 = -3$.

Flashcard 67: How does one interpret a residual value of zero?

Answer: Observed equals predicted value. Perfect prediction with no error at that point.

Flashcard 68: Find the residual for observed $y = 15$ and predicted $\hat{y} = 18$.

Answer: Residual = -3. Using the formula: $15 - 18 = -3$.

Flashcard 69: What does a residual plot with no discernible pattern indicate?

Answer: A good fit for the regression model. Random scatter indicates the model captures the relationship well.

Flashcard 70: Which term describes residuals that display constant spread?

Answer: Homoscedasticity. Equal spread indicates the regression assumptions are met.

Flashcard 71: What does a large residual indicate about the model's prediction?

Answer: Poor prediction accuracy. Large residuals show the model made significant prediction errors.

Flashcard 72: Find the residual if $y = 7$ and $\hat{y} = 7$.

Answer: Residual = 0. Using the formula: $7 - 7 = 0$.

Flashcard 73: What does a pattern in a residual plot suggest about a model?

Answer: The model may be inadequate or misspecified. Patterns suggest the linear model doesn't fit the data properly.

Flashcard 74: What is indicated by residuals tightly clustering around zero?

Answer: Good model fit. Small residuals near zero indicate accurate predictions.

Flashcard 75: Find the residual for $y = 17$ and $\hat{y} = 15$.

Answer: Residual = 2. Using the formula: $17 - 15 = 2$.

Flashcard 76: Which plot is used to detect non-linearity in a model?

Answer: Residual plot. Curved patterns in residuals reveal non-linear relationships.

Flashcard 77: What does a positive residual indicate about the observed value?

Answer: Observed value is greater than predicted value. The model underestimated the actual value.

Flashcard 78: Find the residual for observed $y = 21$ and predicted $\hat{y} = 19$.

Answer: Residual = 2. Using the formula: $21 - 19 = 2$.