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.