9.8: Vocabulary (Chapter 9)
- Page ID
- 59144
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Chapter 9 Vocabulary
- Bivariate Data
- Data that includes two quantitative variables measured for each individual in a study. Often used to examine relationships between variables.
- Scatterplot
- A graph that displays pairs of numerical data as points on a coordinate plane. Each point represents an individual’s value for two variables (x and y).
- Direction of Association
- A description of how one variable tends to change as the other changes. Associations can be positive, negative, or have no clear direction.
- Positive Association
- When values of one variable tend to increase as the values of the other variable also increase. The pattern typically slopes upward from left to right.
- Negative Association
- When values of one variable increase as the other decreases. The pattern typically slopes downward from left to right.
- Correlation (r)
- A numerical measure between –1 and 1 that describes the strength and direction of a linear relationship between two variables. A value close to ±1 indicates a strong linear relationship.
- Correlation Coefficient (r)
- Another name for the correlation measure. It quantifies linear association but does not imply causation.
- Least-Squares Regression Line (LSRL)
- The line that best fits a scatterplot and minimizes the sum of the squared residuals. It models the linear relationship and can be used for prediction.
- Regression Equation
- The formula of the form \( \hat{y} = a + bx \) where \( \hat{y} \) is the predicted value, \( a \) is the intercept, and \( b \) is the slope.
- Slope
- In a regression line, the slope tells how much the predicted value of \( y \) changes for each one-unit increase in \( x \). It represents the rate of change.
- Intercept
- The y-value predicted when \( x = 0 \) in a regression model. It may or may not be meaningful depending on the context and data range.
- Residual
- The difference between an actual data value and the value predicted by a regression model. Residual = actual – predicted.
- Interpolation
- Using a regression model to predict a value within the range of the observed data.
- Extrapolation
- Using a regression model to predict a value outside the range of the observed data. It can be risky because the relationship may not hold beyond the data range.
- Causation
- The idea that one variable has a direct effect on another. Causation implies a change in one variable produces a change in the other. It requires evidence beyond just statistical association.
- Correlation Does Not Imply Causation
- A reminder that even strong relationships between variables do not prove one causes the other. Alternate explanations or lurking variables may be involved.