AP Statistics Flashcards: Representing Relationships Between Two Quantitative Variables

What this deck covers

This deck focuses on Representing Relationships Between Two Quantitative Variables, 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 range of values for the correlation coefficient $r$.

Answer: $-1 \leq r \leq 1$. Correlation is bounded between perfect negative and perfect positive.

Flashcard 2: What is the purpose of transformation in regression?

Answer: Stabilize variance and make data normal. Improves model fit by meeting assumptions.

Flashcard 3: Identify the correlation strength: $r = -0.9$.

Answer: Strong negative. Values near -1 or 1 indicate strong association.

Flashcard 4: Determine the slope $b$ given $r = 0.5$, $s_y = 2$, $s_x = 4$.

Answer: $b = 0.25$. Formula: $b = r \cdot \frac{s_y}{s_x}$ gives slope.

Flashcard 5: Determine the slope $b$ given $r = 0.5$, $s_y = 2$, $s_x = 4$.

Answer: $b = 0.25$. Formula: $b = r \cdot \frac{s_y}{s_x}$ gives slope.

Flashcard 6: State the interpretation of a correlation coefficient $r$ of 0.8.

Answer: Strong positive linear relationship. Values near 1 indicate strong positive linear association.

Flashcard 7: Identify the coefficient of determination and its symbol.

Answer: $R^2$. Measures goodness of fit in regression models.

Flashcard 8: Determine the predicted value for $x = 3$ in $\hat{y} = 4 + 2x$.

Answer: Predicted $y = 10$. Substitute $x$ value into regression equation.

Flashcard 9: Find the residual for $y = 12$, predicted $y = 10$.

Answer: Residual = 2. Simple subtraction: observed minus predicted.

Flashcard 10: Identify the correct interpretation: $R^2 = 0.8$.

Answer: 80% of variance explained by model. Proportion of total variation explained by regression.

Flashcard 11: What is a scatterplot used for in statistics?

Answer: Visualize relationship between two quantitative variables. Shows pattern and strength of association graphically.

Flashcard 12: What is the least squares line for $b = 1.5$, $a = 2$?

Answer: $\hat{y} = 2 + 1.5x$. Standard linear equation form with given parameters.

Flashcard 13: Calculate $R^2$ given $r = 0.6$.

Answer: $R^2 = 0.36$. Coefficient of determination equals correlation squared.

Flashcard 14: What is the role of the $y$-intercept $a$ in a regression line?

Answer: Value of $y$ when $x = 0$. Starting value when explanatory variable equals zero.

Flashcard 15: Find the residual for $y = 10$, $\bar{y} = 8$, predicted $y = 9$.

Answer: Residual = $10 - 9 = 1$. Actual value minus predicted value gives error.

Flashcard 16: What does a residual plot help to assess?

Answer: Linearity and equal variance in regression. Random scatter indicates model assumptions are met.

Flashcard 17: What is the correlation for no linear relationship?

Answer: $r = 0$. Zero indicates absence of linear relationship.

Flashcard 18: Determine if $r = -1.0$ indicates a perfect relationship.

Answer: Yes, perfect negative. Extreme values indicate perfect linear relationships.

Flashcard 19: State the interpretation of a correlation coefficient $r$ of 0.8.

Answer: Strong positive linear relationship. Values near 1 indicate strong positive linear association.

Flashcard 20: Identify the correct interpretation: $R^2 = 0.8$.

Answer: 80% of variance explained by model. Proportion of total variation explained by regression.

Flashcard 21: Find $R^2$ if $r = -0.5$.

Answer: $R^2 = 0.25$. Sign doesn't affect $R^2$ calculation.

Flashcard 22: What is a leverage point in regression analysis?

Answer: Point with extreme value in predictor variable. High leverage can strongly influence regression results.

Flashcard 23: Calculate residual for $y = 15$, $\bar{y} = 10$, predicted $y = 13$.

Answer: Residual = 2. Observed minus predicted gives prediction error.

Flashcard 24: How do you interpret the slope $b$ in a regression line?

Answer: Change in $y$ for a one-unit increase in $x$. Represents rate of change in response variable.

Flashcard 25: Find the residual for $y = 12$, predicted $y = 10$.

Answer: Residual = 2. Simple subtraction: observed minus predicted.

Flashcard 26: Define extrapolation in the context of regression.

Answer: Predicting outside the range of the data. Risky because patterns may not continue beyond data.

Flashcard 27: What does a correlation coefficient $r$ of 0 indicate?

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

Flashcard 28: Calculate $R^2$ given $r = 0.6$.

Answer: $R^2 = 0.36$. Coefficient of determination equals correlation squared.

Flashcard 29: Describe the meaning of a residual in regression analysis.

Answer: Difference between observed and predicted values. Measures prediction error for each observation.

Flashcard 30: What does a residual plot help to assess?

Answer: Linearity and equal variance in regression. Random scatter indicates model assumptions are met.

Flashcard 31: Determine the correlation sign: $r = -0.7$.

Answer: Negative. Negative values indicate downward trend.

Flashcard 32: Calculate residual for $y = 15$, $\bar{y} = 10$, predicted $y = 13$.

Answer: Residual = 2. Observed minus predicted gives prediction error.

Flashcard 33: How do you interpret the slope $b$ in a regression line?

Answer: Change in $y$ for a one-unit increase in $x$. Represents rate of change in response variable.

Flashcard 34: What is the role of the $y$-intercept $a$ in a regression line?

Answer: Value of $y$ when $x = 0$. Starting value when explanatory variable equals zero.

Flashcard 35: Determine the direction of association: $r = 0.6$.

Answer: Positive. Positive correlation indicates upward trend.

Flashcard 36: Find and correct: $r = 1.2$ is possible for correlation.

Answer: Correct: $r$ must be $-1 \leq r \leq 1$. Correlation cannot exceed absolute value of 1.

Flashcard 37: What does the coefficient of determination $R^2$ represent?

Answer: Proportion of variance in $y$ explained by $x$. Indicates how much variation the model explains.

Flashcard 38: Identify the term for a point that significantly affects a regression line.

Answer: Influential point. Has large effect on regression line parameters.

Flashcard 39: What is a leverage point in regression analysis?

Answer: Point with extreme value in predictor variable. High leverage can strongly influence regression results.

Flashcard 40: Identify the correlation strength: $r = -0.9$.

Answer: Strong negative. Values near -1 or 1 indicate strong association.

Flashcard 41: Determine the direction of association: $r = 0.6$.

Answer: Positive. Positive correlation indicates upward trend.

Flashcard 42: Determine the predicted value for $x = 3$ in $\hat{y} = 4 + 2x$.

Answer: Predicted $y = 10$. Substitute $x$ value into regression equation.

Flashcard 43: What is the least squares line for $b = 1.5$, $a = 2$?

Answer: $\hat{y} = 2 + 1.5x$. Standard linear equation form with given parameters.

Flashcard 44: What does the coefficient of determination $R^2$ represent?

Answer: Proportion of variance in $y$ explained by $x$. Indicates how much variation the model explains.

Flashcard 45: Find the $y$-intercept for $\hat{y} = 3 + 4x$.

Answer: $y$-intercept = 3. Constant term is value when $x = 0$.

Flashcard 46: Find the $y$-intercept for $\hat{y} = 3 + 4x$.

Answer: $y$-intercept = 3. Constant term is value when $x = 0$.

Flashcard 47: What is a scatterplot used for in statistics?

Answer: Visualize relationship between two quantitative variables. Shows pattern and strength of association graphically.

Flashcard 48: Identify the range of values for the correlation coefficient $r$.

Answer: $-1 \leq r \leq 1$. Correlation is bounded between perfect negative and perfect positive.

Flashcard 49: Describe the meaning of a residual in regression analysis.

Answer: Difference between observed and predicted values. Measures prediction error for each observation.

Flashcard 50: Identify the correlation type: $r = 0.2$.

Answer: Weak positive. Values near zero indicate weak association.

Flashcard 51: Determine if $r = -1.0$ indicates a perfect relationship.

Answer: Yes, perfect negative. Extreme values indicate perfect linear relationships.

Flashcard 52: Identify the coefficient of determination and its symbol.

Answer: $R^2$. Measures goodness of fit in regression models.

Flashcard 53: Find the residual for $y = 10$, $\bar{y} = 8$, predicted $y = 9$.

Answer: Residual = $10 - 9 = 1$. Actual value minus predicted value gives error.

Flashcard 54: What is the formula for calculating the correlation coefficient $r$?

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

Flashcard 55: Determine the correlation sign: $r = -0.7$.

Answer: Negative. Negative values indicate downward trend.

Flashcard 56: Find $R^2$ if $r = -0.5$.

Answer: $R^2 = 0.25$. Sign doesn't affect $R^2$ calculation.

Flashcard 57: What does a correlation coefficient $r$ of 0 indicate?

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

Flashcard 58: Find and correct: $r = 1.2$ is possible for correlation.

Answer: Correct: $r$ must be $-1 \leq r \leq 1$. Correlation cannot exceed absolute value of 1.

Flashcard 59: Define extrapolation in the context of regression.

Answer: Predicting outside the range of the data. Risky because patterns may not continue beyond data.

Flashcard 60: What is the purpose of transformation in regression?

Answer: Stabilize variance and make data normal. Improves model fit by meeting assumptions.

Flashcard 61: What is the correlation for no linear relationship?

Answer: $r = 0$. Zero indicates absence of linear relationship.

Flashcard 62: Identify the term for a point that significantly affects a regression line.

Answer: Influential point. Has large effect on regression line parameters.

Flashcard 63: What is the formula for the least squares regression line?

Answer: $\hat{y} = a + bx$. Standard form with intercept $a$ and slope $b$.