AP Statistics Chapter 3 Review

Scatterplots and Variables

• Scatterplots visualize the relationship between two quantitative variables.
• The explanatory variable is always represented on the horizontal axis of a scatterplot.

Describing Relationships

• Direction can be classified as positive or negative.
• Outliers are points that lie outside the general pattern of data; clusters group points close together.
• Forms of relationships can either be linear or non-linear.
• Strength of a relationship is characterized by terms such as very strong, moderately strong, or fairly weak.

Correlation

• Correlation measures the strength of a linear relationship between two variables.
• Both variables must be quantitative to determine correlation.
• An R value of 1 indicates a perfect positive correlation; an R value of 0 indicates no correlation.
• Correlation is affected by extreme observations and is not resistant to outliers.

Regression Analysis

• The general form of a regression equation is y(hat) = a + bx, where:
  • y(hat) is the predicted y value,
  • b is the slope,
  • a is the y-intercept.
• The distinction between actual and predicted values is defined as y (actual value) vs. y(hat) (predicted value).
• Extrapolation refers to predictions made outside the range of observed data, which can lead to inaccuracies.

Residual Analysis

• For a well-fitted least squares regression line, the residual plot should show no discernible pattern.
• Residuals represent the difference between actual y-values and predicted y-values and are calculated by y - y(hat).

Associations and Causation

• Associations do not imply causation; correlation between variables does not confirm that they influence each other.

Coefficient and Interpretation

• The coefficient of determination (r²) reflects the percentage of variation in the response variable accounted for by the model.
• The correlation coefficient (r) indicates the strength and direction of a linear relationship and is derived from the square root of r².
• The slope (b) of the regression equation indicates how much the response variable (RV) is expected to change with each unit change in the explanatory variable (EV).
• The y-intercept (a) predicts the value of the RV when the EV is zero.

Value Associations

• R values indicate the strength and direction of associations:
  • R = 0.45 suggests a positive, fairly weak association.
  • R = 0.9 suggests a positive, very strong association.
  • R = -0.3 indicates a negative, fairly weak association.
  • R = -0.8 indicates a negative, very strong association.
  • R = -1 indicates a negative, perfect association.

Test your understanding of scatterplots and relationships between quantitative variables with these flashcards. This quiz covers key concepts related to explanatory variables and the description of data trends, including outliers and clusters. Perfect for AP Statistics students preparing for exams!