AP Statistics Flashcards: Introducing Statistics Do Those Points Align

What this deck covers

This deck focuses on Introducing Statistics Do Those Points Align, 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 does $b_1$ represent in the regression equation?

Answer: The slope of the line. Rate of change in y per unit x.

Flashcard 2: What is an outlier in the context of a scatterplot?

Answer: A data point that does not fit the general pattern of the data. Deviates significantly from the overall trend.

Flashcard 3: What does $r = 1$ imply about the relationship between two variables?

Answer: Perfect positive linear relationship. All points lie exactly on a straight line upward.

Flashcard 4: Identify the axis typically used for the response variable in a scatterplot.

Answer: The y-axis. Convention places dependent variable on vertical axis.

Flashcard 5: Which statistical test is used to determine the significance of a correlation coefficient?

Answer: The t-test. Tests if correlation differs significantly from zero.

Flashcard 6: Identify the formula for calculating the correlation coefficient $r$.

Answer: $r = \frac{\sum((x_i - \bar{x})(y_i - \bar{y}))}{(n-1)s_x s_y}$. Standard formula using means and standard deviations.

Flashcard 7: Identify a method to visually assess normality in residuals of a regression model.

Answer: Normal probability plot. Checks if residuals follow normal distribution.

Flashcard 8: What is the effect of adding a variable with no correlation to the response variable?

Answer: May reduce $R^2$. Irrelevant variables don't improve model fit.

Flashcard 9: What does $b_1$ represent in the regression equation?

Answer: The slope of the line. Rate of change in y per unit x.

Flashcard 10: What is the range of values for the correlation coefficient $r$?

Answer: $-1 \text{ to } 1$. Bounded values indicating strength of linear relationship.

Flashcard 11: What does a negative association in a scatterplot indicate?

Answer: As one variable increases, the other variable decreases. Variables move in opposite directions to each other.

Flashcard 12: Which test checks if a linear relationship exists between two variables?

Answer: Pearson's correlation test. Formal test for linear association significance.

Flashcard 13: Which statistical measure quantifies the strength and direction of a linear relationship?

Answer: The correlation coefficient, $r$. Measures linear association between -1 and 1.

Flashcard 14: What does a positive association in a scatterplot indicate?

Answer: As one variable increases, the other variable also increases. Both variables move in the same direction together.

Flashcard 15: What does $r = -1$ imply about the relationship between two variables?

Answer: Perfect negative linear relationship. All points lie exactly on a straight line downward.

Flashcard 16: What does $r = -1$ imply about the relationship between two variables?

Answer: Perfect negative linear relationship. All points lie exactly on a straight line downward.

Flashcard 17: What is the effect of adding a variable with no correlation to the response variable?

Answer: May reduce $R^2$. Irrelevant variables don't improve model fit.

Flashcard 18: What is the primary use of a linear regression line in a scatterplot?

Answer: To predict values of the response variable. Line enables estimation of unknown y-values.

Flashcard 19: What does a residual plot with no pattern indicate about a regression model?

Answer: The model is appropriate. Random scatter confirms linear model assumptions.

Flashcard 20: State the equation for a simple linear regression line.

Answer: $y = b_0 + b_1x$. Standard form of linear equation with coefficients.

Flashcard 21: What is the range of values for the coefficient of determination $R^2$?

Answer: $0 \text{ to } 1$. Proportion values from 0% to 100% fit.

Flashcard 22: Identify the type of plot used to assess the linearity assumption of a regression model.

Answer: Scatterplot of residuals versus fitted values. Examines residuals to check linear assumption.

Flashcard 23: What does $b_0$ represent in the regression equation?

Answer: The y-intercept. Value of y when x equals zero.

Flashcard 24: What does the term 'homoscedasticity' refer to in a scatterplot?

Answer: Consistent variance of errors across all levels of an independent variable. Equal spread of residuals at all levels.

Flashcard 25: Which concept describes the influence of a single point on a regression line?

Answer: Leverage. Measures how much a point affects line.

Flashcard 26: Which concept describes how well a regression line fits the data?

Answer: Coefficient of determination, $R^2$. Measures proportion of variance explained by model.

Flashcard 27: What does the term 'homoscedasticity' refer to in a scatterplot?

Answer: Consistent variance of errors across all levels of an independent variable. Equal spread of residuals at all levels.

Flashcard 28: What does an $R^2$ value of 0.75 imply?

Answer: 75% of the variability in the response variable is explained by the model. Model explains three-quarters of the variation.

Flashcard 29: What does a negative association in a scatterplot indicate?

Answer: As one variable increases, the other variable decreases. Variables move in opposite directions to each other.

Flashcard 30: What does $r = 0$ imply about the relationship between two variables?

Answer: No linear relationship. Points show no linear pattern or trend.

Flashcard 31: Identify the effect of a high correlation coefficient on prediction accuracy.

Answer: Leads to more accurate predictions. Strong correlation reduces prediction errors.

Flashcard 32: What does $r = 0$ imply about the relationship between two variables?

Answer: No linear relationship. Points show no linear pattern or trend.

Flashcard 33: What does a Cook's distance value greater than 1 suggest?

Answer: The data point may have too much influence on the regression model. Indicates potentially problematic influential observation.

Flashcard 34: Identify a method to visually assess normality in residuals of a regression model.

Answer: Normal probability plot. Checks if residuals follow normal distribution.

Flashcard 35: What does it mean if a scatterplot shows a cluster of points?

Answer: There may be a subset of data behaving differently. Indicates possible subgroups within the data.

Flashcard 36: What is the range of values for the correlation coefficient $r$?

Answer: $-1 \text{ to } 1$. Bounded values indicating strength of linear relationship.

Flashcard 37: What is the range of values for the coefficient of determination $R^2$?

Answer: $0 \text{ to } 1$. Proportion values from 0% to 100% fit.

Flashcard 38: What is an outlier in the context of a scatterplot?

Answer: A data point that does not fit the general pattern of the data. Deviates significantly from the overall trend.

Flashcard 39: Identify the axis typically used for the response variable in a scatterplot.

Answer: The y-axis. Convention places dependent variable on vertical axis.

Flashcard 40: What is the primary use of a linear regression line in a scatterplot?

Answer: To predict values of the response variable. Line enables estimation of unknown y-values.

Flashcard 41: What is multicollinearity in the context of regression analysis?

Answer: High correlation between two or more predictor variables. Creates instability in regression coefficient estimates.

Flashcard 42: Which statistical test is used to determine the significance of a correlation coefficient?

Answer: The t-test. Tests if correlation differs significantly from zero.

Flashcard 43: Which graph is appropriate for visualizing the relationship between categorical variables?

Answer: A bar chart. Categorical data requires bars, not scatterplots.

Flashcard 44: What is the impact of heteroscedasticity on regression analysis?

Answer: Violates the assumption of constant variance. Non-constant variance violates regression assumptions.

Flashcard 45: Which option indicates a non-linear relationship in a scatterplot?

Answer: Curve of best fit. Curved patterns indicate non-linear relationships.

Flashcard 46: Identify the axis typically used for the explanatory variable in a scatterplot.

Answer: The x-axis. Convention places independent variable on horizontal axis.

Flashcard 47: Identify the effect of outliers on the correlation coefficient.

Answer: Can greatly increase or decrease the correlation coefficient. Outliers can dramatically alter correlation values.

Flashcard 48: Identify the effect of outliers on the correlation coefficient.

Answer: Can greatly increase or decrease the correlation coefficient. Outliers can dramatically alter correlation values.

Flashcard 49: Which graph is appropriate for visualizing the relationship between categorical variables?

Answer: A bar chart. Categorical data requires bars, not scatterplots.

Flashcard 50: What does $r = 1$ imply about the relationship between two variables?

Answer: Perfect positive linear relationship. All points lie exactly on a straight line upward.

Flashcard 51: Which option indicates a non-linear relationship in a scatterplot?

Answer: Curve of best fit. Curved patterns indicate non-linear relationships.

Flashcard 52: State the equation for a simple linear regression line.

Answer: $y = b_0 + b_1x$. Standard form of linear equation with coefficients.

Flashcard 53: What is the purpose of a scatterplot in statistics?

Answer: To visually display the relationship between two quantitative variables. Shows how one variable changes as another changes.

Flashcard 54: What does a correlation coefficient close to 0 indicate?

Answer: Weak linear relationship. Little to no linear association between variables.

Flashcard 55: Which concept describes how well a regression line fits the data?

Answer: Coefficient of determination, $R^2$. Measures proportion of variance explained by model.

Flashcard 56: Identify the effect of a high correlation coefficient on prediction accuracy.

Answer: Leads to more accurate predictions. Strong correlation reduces prediction errors.

Flashcard 57: Which term describes a scatterplot where points form a curved pattern?

Answer: Non-linear relationship. Points follow a curve rather than straight line.

Flashcard 58: What does a Cook's distance value greater than 1 suggest?

Answer: The data point may have too much influence on the regression model. Indicates potentially problematic influential observation.

Flashcard 59: Which statistical measure quantifies the strength and direction of a linear relationship?

Answer: The correlation coefficient, $r$. Measures linear association between -1 and 1.

Flashcard 60: Identify the type of plot used to assess the linearity assumption of a regression model.

Answer: Scatterplot of residuals versus fitted values. Examines residuals to check linear assumption.

Flashcard 61: Which concept describes the influence of a single point on a regression line?

Answer: Leverage. Measures how much a point affects line.

Flashcard 62: Which metric measures the spread of residuals around the regression line?

Answer: Standard error of the estimate. Quantifies typical distance from regression line.

Flashcard 63: Which term describes a scatterplot where points form a straight line?

Answer: Linear relationship. Points cluster around an imaginary straight line.

Flashcard 64: Which metric measures the spread of residuals around the regression line?

Answer: Standard error of the estimate. Quantifies typical distance from regression line.

Flashcard 65: What does an $R^2$ value of 0.75 imply?

Answer: 75% of the variability in the response variable is explained by the model. Model explains three-quarters of the variation.

Flashcard 66: Which term describes a scatterplot where points form a curved pattern?

Answer: Non-linear relationship. Points follow a curve rather than straight line.

Flashcard 67: What is the impact of heteroscedasticity on regression analysis?

Answer: Violates the assumption of constant variance. Non-constant variance violates regression assumptions.

Flashcard 68: Which test checks if a linear relationship exists between two variables?

Answer: Pearson's correlation test. Formal test for linear association significance.

Flashcard 69: What does a residual plot with no pattern indicate about a regression model?

Answer: The model is appropriate. Random scatter confirms linear model assumptions.

Flashcard 70: What does a correlation coefficient close to 0 indicate?

Answer: Weak linear relationship. Little to no linear association between variables.

Flashcard 71: Identify the axis typically used for the explanatory variable in a scatterplot.

Answer: The x-axis. Convention places independent variable on horizontal axis.

Flashcard 72: What does it mean if a scatterplot shows a cluster of points?

Answer: There may be a subset of data behaving differently. Indicates possible subgroups within the data.