AP Statistics Flashcards: Analyzing Departures From Linearity

What this deck covers

This deck focuses on Analyzing Departures From Linearity, 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 a residual in the context of linear regression?

Answer: Residual = Observed value - Predicted value. The difference between what actually occurred and what the model predicted.

Flashcard 2: What does a pattern in residuals indicate?

Answer: Indicates a model misfit. Systematic patterns suggest model assumptions are violated.

Flashcard 3: What is the role of residual analysis in regression?

Answer: To check model assumptions. Evaluates whether model meets required assumptions for valid inference.

Flashcard 4: What is a common issue if residuals increase with fitted values?

Answer: Heteroscedasticity. Increasing variance violates constant variance assumption of linear regression.

Flashcard 5: Which transformation can address right skewness?

Answer: Square root transformation. Reduces the effect of large values in right-skewed distributions.

Flashcard 6: How do you identify an influential point in regression?

Answer: Influential points significantly affect the slope. Points with high leverage and large residuals change regression coefficients substantially.

Flashcard 7: What transformation is used for positive skewness?

Answer: Log transformation. Compresses large values more than small ones, reducing right tail.

Flashcard 8: Identify a method for testing linearity in regression analysis.

Answer: Examine the residuals for patterns. Look for systematic patterns that indicate assumption violations.

Flashcard 9: Identify the result of high leverage points in regression.

Answer: Can disproportionately influence the model. Points far from center of predictors can heavily influence fitted line.

Flashcard 10: What is the impact of non-linearity on predictions?

Answer: Leads to inaccurate predictions. Linear model cannot capture true relationship, causing prediction errors.

Flashcard 11: What does a residual plot with increasing spread indicate?

Answer: Non-constant variance. Spread increases with fitted values, violating homoscedasticity assumption.

Flashcard 12: Which pattern in residuals suggests a transformation is needed?

Answer: Non-random pattern. Systematic structure indicates linear model is inadequate.

Flashcard 13: What does a lack of randomness in residuals suggest?

Answer: Model assumptions are violated. Systematic patterns indicate linear model is inappropriate for the data.

Flashcard 14: What pattern in residuals suggests a better fit with a quadratic model?

Answer: Curved pattern. U-shaped residuals indicate relationship has quadratic component.

Flashcard 15: Identify the formula for calculating a residual.

Answer: $e_i = y_i - \bar{y}_i$. Where $e_i$ is residual, $y_i$ is observed, and $\bar{y}_i$ is predicted value.

Flashcard 16: What is the effect of non-linearity on model accuracy?

Answer: Reduces model accuracy. Linear model cannot capture true relationship, leading to systematic errors.

Flashcard 17: Which plot can help identify non-linearity in data?

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

Flashcard 18: Which assumption is violated if residuals show a funnel shape?

Answer: Homoscedasticity is violated. Funnel shape indicates variance increases with fitted values.

Flashcard 19: What is a residual in the context of linear regression?

Answer: Residual = Observed value - Predicted value. The difference between what actually occurred and what the model predicted.

Flashcard 20: What method can address the issue of non-linearity?

Answer: Transformation of variables. Mathematical functions applied to create linear relationships from non-linear data.

Flashcard 21: What does a residual plot with no apparent pattern indicate?

Answer: Assumptions likely satisfied. Random scatter confirms linear model is appropriate for the data.

Flashcard 22: Identify the effect of outliers on a regression line.

Answer: Outliers can skew the regression line. Extreme values pull the line away from the true relationship.

Flashcard 23: What does a lack of randomness in residuals suggest?

Answer: Model assumptions are violated. Systematic patterns indicate linear model is inappropriate for the data.

Flashcard 24: What does a pattern in residuals indicate?

Answer: Indicates a model misfit. Systematic patterns suggest model assumptions are violated.

Flashcard 25: Which plot can help identify non-linearity in data?

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

Flashcard 26: Identify the result of high leverage points in regression.

Answer: Can disproportionately influence the model. Points far from center of predictors can heavily influence fitted line.

Flashcard 27: What does a random pattern in a residual plot indicate?

Answer: Random pattern indicates a good fit. No systematic patterns suggest linear model assumptions are met.

Flashcard 28: Which transformation can stabilize variance in a dataset?

Answer: Logarithmic transformation. Reduces variability when variance increases with the mean.

Flashcard 29: What does a residual plot display?

Answer: Residual plot displays residuals vs. fitted values. Shows errors on y-axis and predicted values on x-axis to check assumptions.

Flashcard 30: What does a linear pattern in residuals suggest about the model?

Answer: Model is not appropriate. Linear trend in residuals indicates model structure is wrong.

Flashcard 31: Identify a common method to address non-linearity.

Answer: Using polynomial regression. Adds curved terms to capture non-linear relationships in data.

Flashcard 32: What method can address the issue of non-linearity?

Answer: Transformation of variables. Mathematical functions applied to create linear relationships from non-linear data.

Flashcard 33: What pattern in residuals suggests a better fit with a quadratic model?

Answer: Curved pattern. U-shaped residuals indicate relationship has quadratic component.

Flashcard 34: What is the purpose of a normal probability plot of residuals?

Answer: To assess normality of residuals. Checks if errors follow normal distribution as required by assumptions.

Flashcard 35: What is examined to ensure the linear model is appropriate?

Answer: Residual plot. Checks whether linear relationship assumption is reasonable for data.

Flashcard 36: What is the effect of random residuals on a regression model?

Answer: Indicates a good fit. No patterns suggest linear model assumptions are satisfied.

Flashcard 37: What transformation is used for positive skewness?

Answer: Log transformation. Compresses large values more than small ones, reducing right tail.

Flashcard 38: Which transformation can stabilize variance in a dataset?

Answer: Logarithmic transformation. Reduces variability when variance increases with the mean.

Flashcard 39: What is a sign of a good regression model in a residual plot?

Answer: No discernible pattern in residuals. Random scatter indicates model captures the relationship appropriately.

Flashcard 40: What does a residual plot with no apparent pattern indicate?

Answer: Assumptions likely satisfied. Random scatter confirms linear model is appropriate for the data.

Flashcard 41: Which pattern in residuals suggests the need for a polynomial model?

Answer: Curved pattern. U-shaped pattern indicates quadratic relationship exists in data.

Flashcard 42: What is a sign of a good regression model in a residual plot?

Answer: No discernible pattern in residuals. Random scatter indicates model captures the relationship appropriately.

Flashcard 43: Which transformation can address right skewness?

Answer: Square root transformation. Reduces the effect of large values in right-skewed distributions.

Flashcard 44: What does a residual of zero indicate?

Answer: Observed value equals predicted value. Perfect prediction with no error between observed and fitted values.

Flashcard 45: What does heteroscedasticity in a residual plot indicate?

Answer: Indicates non-constant variance. Error variance changes across fitted values, violating equal variance assumption.

Flashcard 46: What is the impact of non-linearity on predictions?

Answer: Leads to inaccurate predictions. Linear model cannot capture true relationship, causing prediction errors.

Flashcard 47: What graphical tool is used to check linearity assumptions?

Answer: Residual plot. Primary diagnostic tool for evaluating whether linear model assumptions hold.

Flashcard 48: What does heteroscedasticity in a residual plot indicate?

Answer: Indicates non-constant variance. Error variance changes across fitted values, violating equal variance assumption.

Flashcard 49: Identify a method for testing linearity in regression analysis.

Answer: Examine the residuals for patterns. Look for systematic patterns that indicate assumption violations.

Flashcard 50: Identify a common method to address non-linearity.

Answer: Using polynomial regression. Adds curved terms to capture non-linear relationships in data.

Flashcard 51: How do you identify an influential point in regression?

Answer: Influential points significantly affect the slope. Points with high leverage and large residuals change regression coefficients substantially.

Flashcard 52: Identify a technique to improve model fit with non-linear data.

Answer: Use transformations. Mathematical functions applied to variables to create linear relationships.

Flashcard 53: Identify the role of transformations in linear regression.

Answer: To linearize relationships and stabilize variance. Creates linear relationships and meets regression assumptions.

Flashcard 54: What is the role of residual analysis in regression?

Answer: To check model assumptions. Evaluates whether model meets required assumptions for valid inference.

Flashcard 55: Identify the role of transformations in linear regression.

Answer: To linearize relationships and stabilize variance. Creates linear relationships and meets regression assumptions.

Flashcard 56: What does a curved pattern in a residual plot suggest?

Answer: Curved pattern suggests non-linearity. Indicates the relationship is not linear and needs a different model form.

Flashcard 57: What does a linear pattern in residuals suggest about the model?

Answer: Model is not appropriate. Linear trend in residuals indicates model structure is wrong.

Flashcard 58: Identify a technique to improve model fit with non-linear data.

Answer: Use transformations. Mathematical functions applied to variables to create linear relationships.

Flashcard 59: Which pattern in residuals suggests a transformation is needed?

Answer: Non-random pattern. Systematic structure indicates linear model is inadequate.

Flashcard 60: What does a pattern in a residual plot reveal about a model?

Answer: Model may not be appropriate. Patterns indicate linear assumptions are violated and model needs modification.

Flashcard 61: Which pattern in residuals suggests the need for a polynomial model?

Answer: Curved pattern. U-shaped pattern indicates quadratic relationship exists in data.

Flashcard 62: What does a curved pattern in a residual plot suggest?

Answer: Curved pattern suggests non-linearity. Indicates the relationship is not linear and needs a different model form.

Flashcard 63: Identify the formula for calculating a residual.

Answer: $e_i = y_i - \bar{y}_i$. Where $e_i$ is residual, $y_i$ is observed, and $\bar{y}_i$ is predicted value.

Flashcard 64: What is examined to ensure the linear model is appropriate?

Answer: Residual plot. Checks whether linear relationship assumption is reasonable for data.

Flashcard 65: What graphical tool is used to check linearity assumptions?

Answer: Residual plot. Primary diagnostic tool for evaluating whether linear model assumptions hold.

Flashcard 66: What is a common issue if residuals increase with fitted values?

Answer: Heteroscedasticity. Increasing variance violates constant variance assumption of linear regression.

Flashcard 67: What does a residual plot with increasing spread indicate?

Answer: Non-constant variance. Spread increases with fitted values, violating homoscedasticity assumption.

Flashcard 68: What does a pattern in a residual plot reveal about a model?

Answer: Model may not be appropriate. Patterns indicate linear assumptions are violated and model needs modification.

Flashcard 69: What is the effect of random residuals on a regression model?

Answer: Indicates a good fit. No patterns suggest linear model assumptions are satisfied.

Flashcard 70: What is the purpose of a normal probability plot of residuals?

Answer: To assess normality of residuals. Checks if errors follow normal distribution as required by assumptions.

Flashcard 71: What does a random pattern in a residual plot indicate?

Answer: Random pattern indicates a good fit. No systematic patterns suggest linear model assumptions are met.

Flashcard 72: Which assumption is violated if residuals show a funnel shape?

Answer: Homoscedasticity is violated. Funnel shape indicates variance increases with fitted values.

Flashcard 73: What is the effect of non-linearity on model accuracy?

Answer: Reduces model accuracy. Linear model cannot capture true relationship, leading to systematic errors.

Flashcard 74: What does a residual plot display?

Answer: Residual plot displays residuals vs. fitted values. Shows errors on y-axis and predicted values on x-axis to check assumptions.

Flashcard 75: What does a residual of zero indicate?

Answer: Observed value equals predicted value. Perfect prediction with no error between observed and fitted values.

Flashcard 76: Identify the effect of outliers on a regression line.

Answer: Outliers can skew the regression line. Extreme values pull the line away from the true relationship.