Correlation - AP Statistics

1. Identify the correlation type: $r = -0.85$.

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

2. What statistical test is used for testing correlation significance?

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

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

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

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

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

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

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

6. Identify the correlation type: $r = 0.8$.

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

7. State one limitation of using correlation.

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

8. What is the range of the correlation coefficient $r$?

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

9. What does $r = 1$ signify in terms of correlation?

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

10. Identify the correlation type: $r = 0.65$.

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

11. What does a correlation of $r = 0.3$ indicate?

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

12. State the effect of a non-linear relationship on correlation.

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

13. State one assumption for using Pearson's correlation coefficient.

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

14. Find the correlation type for $r = 0.95$.

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

15. What does a correlation coefficient of $r = 0$ indicate?

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

16. Find the correlation type for $r = -0.1$.

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

17. What is the symbol for the population correlation coefficient?

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

18. Does correlation measure the strength of non-linear relationships?

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

19. What is an outlier's effect on correlation?

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

20. What is the primary purpose of correlation analysis?

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

21. What is a scatterplot used for in correlation?

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

22. What is the implication of a high negative correlation?

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

23. What is the effect of a restricted range on correlation?

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

24. Identify the correlation type: $r = -0.9$.

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

25. Identify the correlation type: $r = 0.48$.

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

26. What is the effect of heteroscedasticity on correlation?

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

27. What is the effect of correlation on prediction?

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

28. What correlation type is indicated by $r = -0.7$?

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

29. What is the definition of correlation?

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

30. What is the correlation coefficient's sensitivity to units?

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

31. What does a correlation of $r = -0.5$ indicate?

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

32. Does correlation imply causation?

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

33. What does $r^2$ represent in correlation analysis?

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

34. What correlation type is indicated by $r = 0.5$?

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

35. What is spurious correlation?

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

36. What is the implication of a high positive correlation?

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

37. Identify the correlation type: $r = -0.4$.

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

38. What does a correlation matrix show?

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

39. Identify the correlation type: $r = 0.2$.

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

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