AP Statistics Flashcards: Correlation

What this deck covers

This deck focuses on Correlation, 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: Identify the correlation type: $r = -0.85$.

Answer: Strong negative correlation. Close to -1 indicates strong negative linear relationship.

Flashcard 2: What statistical test is used for testing correlation significance?

Answer: The Pearson correlation significance test. Tests if population correlation differs from zero.

Flashcard 3: What is the formula for the sample correlation coefficient $r$?

Answer: $r = \frac{\sum((x_i - \bar{x})(y_i - \bar{y}))}{\sqrt{\sum(x_i - \bar{x})^2 \cdot \sum(y_i - \bar{y})^2}}$. Standardized covariance using sample standard deviations.

Flashcard 4: What does $r = -1$ signify in terms of correlation?

Answer: Perfect negative linear correlation. All points lie exactly on a negative-sloped line.

Flashcard 5: Choose the correct correlation for $r = 0.0$.

Answer: No linear correlation. Exactly zero means no linear relationship exists.

Flashcard 6: State one assumption for using Pearson's correlation coefficient.

Answer: Variables should have a linear relationship. Pearson's $r$ requires approximately linear relationships.

Flashcard 7: State one limitation of using correlation.

Answer: It does not account for causality. Cannot determine which variable influences the other.

Flashcard 8: Identify the correlation type: $r = 0.8$.

Answer: Strong positive correlation. Close to 1 indicates strong positive linear relationship.

Flashcard 9: State one limitation of using correlation.

Answer: It does not account for causality. Cannot determine which variable influences the other.

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

Answer: $-1 \text{ to } 1$. Bounded range where extremes indicate perfect correlation.

Flashcard 11: What does $r = 1$ signify in terms of correlation?

Answer: Perfect positive linear correlation. All points lie exactly on a positive-sloped line.

Flashcard 12: Identify the correlation type: $r = 0.65$.

Answer: Moderate to strong positive correlation. Between moderate and strong positive correlation range.

Flashcard 13: What does a correlation of $r = 0.3$ indicate?

Answer: Weak positive correlation. Weak but positive linear association between variables.

Flashcard 14: What is spurious correlation?

Answer: A correlation that appears real but is caused by a third variable. Confounding variables create misleading correlations.

Flashcard 15: State the effect of a non-linear relationship on correlation.

Answer: Correlation may underestimate the relationship. Non-linear patterns reduce apparent correlation strength.

Flashcard 16: What is the effect of a restricted range on correlation?

Answer: It can lead to underestimating the true correlation. Limited data range reduces correlation variability.

Flashcard 17: State one assumption for using Pearson's correlation coefficient.

Answer: Variables should have a linear relationship. Pearson's $r$ requires approximately linear relationships.

Flashcard 18: Find the correlation type for $r = 0.95$.

Answer: Very strong positive correlation. Extremely close to 1 indicates nearly perfect positive relationship.

Flashcard 19: What does a correlation coefficient of $r = 0$ indicate?

Answer: No linear relationship between variables. Zero correlation means no linear pattern exists.

Flashcard 20: What is a scatterplot used for in correlation?

Answer: To visually assess the relationship between two variables. Graphically displays correlation patterns and outliers.

Flashcard 21: Find the correlation type for $r = -0.1$.

Answer: Weak negative correlation. Very close to zero indicates minimal linear relationship.

Flashcard 22: What is the effect of heteroscedasticity on correlation?

Answer: It can make correlation less reliable. Unequal variances can affect correlation reliability.

Flashcard 23: What is the symbol for the population correlation coefficient?

Answer: $\rho$ (rho). Greek letter rho represents population parameter.

Flashcard 24: What is the symbol for the population correlation coefficient?

Answer: $\rho$ (rho). Greek letter rho represents population parameter.

Flashcard 25: Does correlation measure the strength of non-linear relationships?

Answer: No, it measures only linear relationships. Only detects linear relationships, not curves.

Flashcard 26: What correlation type is indicated by $r = 0.5$?

Answer: Moderate positive correlation. Halfway between zero and one indicates moderate strength.

Flashcard 27: Identify the correlation type: $r = -0.9$.

Answer: Strong negative correlation. Close to -1 indicates strong negative linear relationship.

Flashcard 28: What is the range of the correlation coefficient $r$?

Answer: $-1 \text{ to } 1$. Bounded range where extremes indicate perfect correlation.

Flashcard 29: What does a correlation coefficient of $r = 0$ indicate?

Answer: No linear relationship between variables. Zero correlation means no linear pattern exists.

Flashcard 30: Choose the correct correlation for $r = 0.0$.

Answer: No linear correlation. Exactly zero means no linear relationship exists.

Flashcard 31: What does $r = -1$ signify in terms of correlation?

Answer: Perfect negative linear correlation. All points lie exactly on a negative-sloped line.

Flashcard 32: What correlation type is indicated by $r = -0.7$?

Answer: Moderate to strong negative correlation. Between moderate and strong negative correlation range.

Flashcard 33: What is an outlier's effect on correlation?

Answer: It can significantly distort the correlation coefficient. Outliers can inflate or deflate correlation strength.

Flashcard 34: What is an outlier's effect on correlation?

Answer: It can significantly distort the correlation coefficient. Outliers can inflate or deflate correlation strength.

Flashcard 35: Does correlation imply causation?

Answer: No, correlation does not imply causation. Association does not establish cause-and-effect relationship.

Flashcard 36: What is the primary purpose of correlation analysis?

Answer: To assess the strength and direction of a linear relationship. Main goal is quantifying linear association strength.

Flashcard 37: What is a scatterplot used for in correlation?

Answer: To visually assess the relationship between two variables. Graphically displays correlation patterns and outliers.

Flashcard 38: What is the implication of a high negative correlation?

Answer: As one variable increases, the other tends to decrease. Strong negative correlation shows variables move opposite.

Flashcard 39: What is the effect of a restricted range on correlation?

Answer: It can lead to underestimating the true correlation. Limited data range reduces correlation variability.

Flashcard 40: What does a correlation matrix show?

Answer: The correlation coefficients between multiple variables. Displays all pairwise correlations in table format.

Flashcard 41: Identify the correlation type: $r = -0.9$.

Answer: Strong negative correlation. Close to -1 indicates strong negative linear relationship.

Flashcard 42: Identify the correlation type: $r = 0.48$.

Answer: Moderate positive correlation. Close to 0.5 indicates moderate positive linear relationship.

Flashcard 43: What is the effect of heteroscedasticity on correlation?

Answer: It can make correlation less reliable. Unequal variances can affect correlation reliability.

Flashcard 44: What does a correlation of $r = 0.3$ indicate?

Answer: Weak positive correlation. Weak but positive linear association between variables.

Flashcard 45: What is the effect of correlation on prediction?

Answer: Stronger correlation improves prediction accuracy. Higher correlation improves predictive model accuracy.

Flashcard 46: Find the correlation type for $r = -0.1$.

Answer: Weak negative correlation. Very close to zero indicates minimal linear relationship.

Flashcard 47: What correlation type is indicated by $r = -0.7$?

Answer: Moderate to strong negative correlation. Between moderate and strong negative correlation range.

Flashcard 48: What is the definition of correlation?

Answer: Correlation measures the strength and direction of a linear relationship between two variables. Quantifies linear association between two quantitative variables.

Flashcard 49: What is the correlation coefficient's sensitivity to units?

Answer: It is unitless and unaffected by unit changes. Standardized measure independent of measurement units.

Flashcard 50: What does $r = 1$ signify in terms of correlation?

Answer: Perfect positive linear correlation. All points lie exactly on a positive-sloped line.

Flashcard 51: What does a correlation of $r = -0.5$ indicate?

Answer: Moderate negative correlation. Exactly halfway between zero and perfect negative correlation.

Flashcard 52: Identify the correlation type: $r = 0.8$.

Answer: Strong positive correlation. Close to 1 indicates strong positive linear relationship.

Flashcard 53: Identify the correlation type: $r = 0.65$.

Answer: Moderate to strong positive correlation. Between moderate and strong positive correlation range.

Flashcard 54: What is the primary purpose of correlation analysis?

Answer: To assess the strength and direction of a linear relationship. Main goal is quantifying linear association strength.

Flashcard 55: What is the effect of correlation on prediction?

Answer: Stronger correlation improves prediction accuracy. Higher correlation improves predictive model accuracy.

Flashcard 56: Does correlation measure the strength of non-linear relationships?

Answer: No, it measures only linear relationships. Only detects linear relationships, not curves.

Flashcard 57: Does correlation imply causation?

Answer: No, correlation does not imply causation. Association does not establish cause-and-effect relationship.

Flashcard 58: What does $r^2$ represent in correlation analysis?

Answer: Proportion of variance explained by the relationship. Squared correlation shows shared variance between variables.

Flashcard 59: What correlation type is indicated by $r = 0.5$?

Answer: Moderate positive correlation. Halfway between zero and one indicates moderate strength.

Flashcard 60: What does a correlation of $r = -0.5$ indicate?

Answer: Moderate negative correlation. Exactly halfway between zero and perfect negative correlation.

Flashcard 61: What is spurious correlation?

Answer: A correlation that appears real but is caused by a third variable. Confounding variables create misleading correlations.

Flashcard 62: Identify the correlation type: $r = -0.85$.

Answer: Strong negative correlation. Close to -1 indicates strong negative linear relationship.

Flashcard 63: What statistical test is used for testing correlation significance?

Answer: The Pearson correlation significance test. Tests if population correlation differs from zero.

Flashcard 64: What is the implication of a high positive correlation?

Answer: As one variable increases, the other tends to increase. Strong positive correlation shows variables move together.

Flashcard 65: Identify the correlation type: $r = -0.4$.

Answer: Moderate negative correlation. Negative value with moderate distance from zero.

Flashcard 66: What is the implication of a high negative correlation?

Answer: As one variable increases, the other tends to decrease. Strong negative correlation shows variables move opposite.

Flashcard 67: What is the formula for the sample correlation coefficient $r$?

Answer: $r = \frac{\sum((x_i - \bar{x})(y_i - \bar{y}))}{\sqrt{\sum(x_i - \bar{x})^2 \cdot \sum(y_i - \bar{y})^2}}$. Standardized covariance using sample standard deviations.

Flashcard 68: What is the definition of correlation?

Answer: Correlation measures the strength and direction of a linear relationship between two variables. Quantifies linear association between two quantitative variables.

Flashcard 69: State the effect of a non-linear relationship on correlation.

Answer: Correlation may underestimate the relationship. Non-linear patterns reduce apparent correlation strength.

Flashcard 70: Find the correlation type for $r = 0.95$.

Answer: Very strong positive correlation. Extremely close to 1 indicates nearly perfect positive relationship.

Flashcard 71: What is the implication of a high positive correlation?

Answer: As one variable increases, the other tends to increase. Strong positive correlation shows variables move together.

Flashcard 72: What is the correlation coefficient's sensitivity to units?

Answer: It is unitless and unaffected by unit changes. Standardized measure independent of measurement units.

Flashcard 73: Identify the correlation type: $r = 0.2$.

Answer: Weak positive correlation. Close to zero indicates weak linear association.

Flashcard 74: What does a correlation matrix show?

Answer: The correlation coefficients between multiple variables. Displays all pairwise correlations in table format.

Flashcard 75: Identify the correlation type: $r = 0.2$.

Answer: Weak positive correlation. Close to zero indicates weak linear association.

Flashcard 76: Identify the correlation type: $r = -0.4$.

Answer: Moderate negative correlation. Negative value with moderate distance from zero.