AP Statistics Flashcards: Introducing Statistics Are Variables Related

What this deck covers

This deck focuses on Introducing Statistics Are Variables Related, 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 the definition of a dependent variable in statistics?

Answer: A variable affected by changes in the independent variable. It responds to changes in the independent variable.

Flashcard 2: Find the correlation: All points on a scatter plot lie on a horizontal line.

Answer: No correlation. Horizontal line shows no relationship between variables.

Flashcard 3: State the formula for the chi-square statistic.

Answer: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$. Compares observed and expected frequencies.

Flashcard 4: What is the definition of a dependent variable in statistics?

Answer: A variable affected by changes in the independent variable. It responds to changes in the independent variable.

Flashcard 5: What type of plot helps detect non-linearity in relationships?

Answer: Residual plot. Patterns in residuals reveal model inadequacies.

Flashcard 6: What does it mean if the residual plot shows a pattern?

Answer: Model may not be appropriate. Patterns suggest violations of regression assumptions.

Flashcard 7: Find the correlation coefficient range for a strong negative relationship.

Answer: Between -1 and -0.7. Values near -1 indicate strong negative association.

Flashcard 8: What does the slope of a regression line indicate?

Answer: The rate of change of the dependent variable per unit change in the independent variable. Shows how much $y$ changes per unit increase in $x$.

Flashcard 9: Find the correlation coefficient range for a strong negative relationship.

Answer: Between -1 and -0.7. Values near -1 indicate strong negative association.

Flashcard 10: Find the $R^2$ value indicating perfect explanatory power.

Answer: $R^2 = 1$. Model explains all the variability.

Flashcard 11: Identify the type of relationship: Both variables increase together.

Answer: Positive correlation. Both variables move in the same direction.

Flashcard 12: Identify the type of relationship: One variable increases while the other decreases.

Answer: Negative correlation. Variables move in opposite directions.

Flashcard 13: What is the null hypothesis in a test for independence between two variables?

Answer: The variables are independent. Assumes no association between the variables.

Flashcard 14: Find the correlation coefficient range for a strong positive relationship.

Answer: Between 0.7 and 1. Values near 1 indicate strong positive association.

Flashcard 15: Find the $R^2$ value indicating no explanatory power.

Answer: $R^2 = 0$. Model explains none of the variability.

Flashcard 16: What does a high $p$-value indicate in a test for correlation?

Answer: Weak evidence against the null hypothesis. Less likely to reject null of no correlation.

Flashcard 17: State the formula for calculating the correlation coefficient $r$.

Answer: $r = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sqrt{\sum{(x_i - \bar{x})^2} \sum{(y_i - \bar{y})^2}}}$. Standardized covariance divided by product of standard deviations.

Flashcard 18: Identify the correlation: Scatter plot points are widely scattered with no pattern.

Answer: No correlation. Points show no discernible linear pattern.

Flashcard 19: What is the meaning of a correlation coefficient of 1?

Answer: Perfect positive linear relationship. All points lie on a perfectly upward-sloping line.

Flashcard 20: What is the purpose of a residual plot in regression analysis?

Answer: To assess the fit of the regression model. Shows whether model assumptions are satisfied.

Flashcard 21: Identify the type of relationship: Both variables increase together.

Answer: Positive correlation. Both variables move in the same direction.

Flashcard 22: Which variable is plotted on the y-axis in a scatter plot?

Answer: Dependent variable. By convention, the response variable goes on y-axis.

Flashcard 23: What statistical method predicts the value of a dependent variable?

Answer: Regression analysis. Uses relationships to make predictions about outcomes.

Flashcard 24: What does a low $p$-value indicate in a test for correlation?

Answer: Strong evidence against the null hypothesis. More likely to reject null of no correlation.

Flashcard 25: What is the Spearman rank correlation coefficient used for?

Answer: Measuring the strength and direction of a monotonic relationship. Works with ranked data instead of raw values.

Flashcard 26: Identify the error: Assuming correlation implies causation.

Answer: Correlation does not imply causation. Association doesn't prove one variable causes another.

Flashcard 27: Identify the type of relationship: One variable increases while the other decreases.

Answer: Negative correlation. Variables move in opposite directions.

Flashcard 28: What type of plot helps detect non-linearity in relationships?

Answer: Residual plot. Patterns in residuals reveal model inadequacies.

Flashcard 29: Find the $R^2$ value indicating no explanatory power.

Answer: $R^2 = 0$. Model explains none of the variability.

Flashcard 30: What is the term for variables that show a relationship in a scatter plot?

Answer: Correlated variables. Variables that show association in their values.

Flashcard 31: What is multicollinearity in the context of regression analysis?

Answer: When independent variables are highly correlated. Creates problems for interpreting individual variable effects.

Flashcard 32: Which statistical test is used to determine if two variables are independent?

Answer: Chi-square test. Tests whether categorical variables are related.

Flashcard 33: Identify the correlation: Scatter plot points lie close to an upward-sloping line.

Answer: Strong positive correlation. Points cluster tightly around an increasing trend.

Flashcard 34: Which variable is plotted on the x-axis in a scatter plot?

Answer: Independent variable. By convention, the explanatory variable goes on x-axis.

Flashcard 35: What is multicollinearity in the context of regression analysis?

Answer: When independent variables are highly correlated. Creates problems for interpreting individual variable effects.

Flashcard 36: What statistical method predicts the value of a dependent variable?

Answer: Regression analysis. Uses relationships to make predictions about outcomes.

Flashcard 37: Which coefficient measures the strength and direction of a linear relationship?

Answer: Pearson correlation coefficient. Quantifies linear association strength and direction.

Flashcard 38: What is the significance of the intercept in a regression equation?

Answer: The expected value of the dependent variable when the independent variable is zero. Starting value when predictor equals zero.

Flashcard 39: What is the term for variables that show a relationship in a scatter plot?

Answer: Correlated variables. Variables that show association in their values.

Flashcard 40: Which variable is plotted on the x-axis in a scatter plot?

Answer: Independent variable. By convention, the explanatory variable goes on x-axis.

Flashcard 41: What is the definition of an independent variable in statistics?

Answer: A variable that is manipulated to observe its effect on a dependent variable. It's controlled by the researcher to study its effects.

Flashcard 42: Find the correlation coefficient range for a strong positive relationship.

Answer: Between 0.7 and 1. Values near 1 indicate strong positive association.

Flashcard 43: What is the alternative hypothesis in a test for independence between two variables?

Answer: The variables are not independent. Claims there is an association between variables.

Flashcard 44: What is the meaning of a correlation coefficient of -1?

Answer: Perfect negative linear relationship. All points lie on a perfectly downward-sloping line.

Flashcard 45: Identify the correlation: Scatter plot points lie close to an upward-sloping line.

Answer: Strong positive correlation. Points cluster tightly around an increasing trend.

Flashcard 46: What does the slope of a regression line indicate?

Answer: The rate of change of the dependent variable per unit change in the independent variable. Shows how much $y$ changes per unit increase in $x$.

Flashcard 47: What is the purpose of a residual plot in regression analysis?

Answer: To assess the fit of the regression model. Shows whether model assumptions are satisfied.

Flashcard 48: What is the null hypothesis in a test for independence between two variables?

Answer: The variables are independent. Assumes no association between the variables.

Flashcard 49: Which term describes a correlation due to a third variable?

Answer: Spurious correlation. False correlation caused by confounding variable.

Flashcard 50: What type of plot is typically used to visualize relationships between two variables?

Answer: Scatter plot. Shows the association pattern between two quantitative variables.

Flashcard 51: What type of plot is typically used to visualize relationships between two variables?

Answer: Scatter plot. Shows the association pattern between two quantitative variables.

Flashcard 52: What is the meaning of a correlation coefficient of 1?

Answer: Perfect positive linear relationship. All points lie on a perfectly upward-sloping line.

Flashcard 53: What is the definition of an independent variable in statistics?

Answer: A variable that is manipulated to observe its effect on a dependent variable. It's controlled by the researcher to study its effects.

Flashcard 54: Identify the correlation: Scatter plot points are widely scattered with no pattern.

Answer: No correlation. Points show no discernible linear pattern.

Flashcard 55: State the formula for calculating the correlation coefficient $r$.

Answer: $r = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sqrt{\sum{(x_i - \bar{x})^2} \sum{(y_i - \bar{y})^2}}}$. Standardized covariance divided by product of standard deviations.

Flashcard 56: What does a low $p$-value indicate in a test for correlation?

Answer: Strong evidence against the null hypothesis. More likely to reject null of no correlation.

Flashcard 57: Which variable is plotted on the y-axis in a scatter plot?

Answer: Dependent variable. By convention, the response variable goes on y-axis.

Flashcard 58: Define causal relationship in statistics.

Answer: A relationship where one variable directly affects another. Changes in one variable cause changes in another.

Flashcard 59: State the formula for the chi-square statistic.

Answer: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$. Compares observed and expected frequencies.

Flashcard 60: What does a high $p$-value indicate in a test for correlation?

Answer: Weak evidence against the null hypothesis. Less likely to reject null of no correlation.

Flashcard 61: What does it mean if the residual plot shows a pattern?

Answer: Model may not be appropriate. Patterns suggest violations of regression assumptions.

Flashcard 62: What is the alternative hypothesis in a test for independence between two variables?

Answer: The variables are not independent. Claims there is an association between variables.

Flashcard 63: Identify the error: Assuming correlation implies causation.

Answer: Correlation does not imply causation. Association doesn't prove one variable causes another.

Flashcard 64: Find the $R^2$ value indicating perfect explanatory power.

Answer: $R^2 = 1$. Model explains all the variability.

Flashcard 65: Which term describes a correlation due to a third variable?

Answer: Spurious correlation. False correlation caused by confounding variable.

Flashcard 66: Define causal relationship in statistics.

Answer: A relationship where one variable directly affects another. Changes in one variable cause changes in another.

Flashcard 67: Which statistical test is used to determine if two variables are independent?

Answer: Chi-square test. Tests whether categorical variables are related.

Flashcard 68: What is the significance of the intercept in a regression equation?

Answer: The expected value of the dependent variable when the independent variable is zero. Starting value when predictor equals zero.

Flashcard 69: What does a correlation coefficient of 0 indicate?

Answer: No linear relationship. Variables have no linear association.

Flashcard 70: What is the role of the coefficient of determination $R^2$?

Answer: It measures the proportion of variance in the dependent variable explained by the model. Higher $R^2$ means better model fit.

Flashcard 71: Find the correlation: All points on a scatter plot lie on a horizontal line.

Answer: No correlation. Horizontal line shows no relationship between variables.

Flashcard 72: What is the meaning of a correlation coefficient of -1?

Answer: Perfect negative linear relationship. All points lie on a perfectly downward-sloping line.

Flashcard 73: What is the Spearman rank correlation coefficient used for?

Answer: Measuring the strength and direction of a monotonic relationship. Works with ranked data instead of raw values.

Flashcard 74: What is the role of the coefficient of determination $R^2$?

Answer: It measures the proportion of variance in the dependent variable explained by the model. Higher $R^2$ means better model fit.

Flashcard 75: What is the meaning of a residual in regression analysis?

Answer: The difference between observed and predicted values. Measures prediction error for each data point.

Flashcard 76: Which coefficient measures the strength and direction of a linear relationship?

Answer: Pearson correlation coefficient. Quantifies linear association strength and direction.

Flashcard 77: What is the meaning of a residual in regression analysis?

Answer: The difference between observed and predicted values. Measures prediction error for each data point.