Chapter 2 (all)

Associated Variables

Two variables are associated if knowing the value of one variable provides information about the value of the other.

Response Variable

The dependent variable that measures the outcome of a study.

Explanatory Variable

The independent variable that explains or causes changes in the response variable.

Variables

Characteristics or properties that can vary and are measured in statistical studies.

Statistical Studies

Research investigations that analyze data to identify relationships between variables.

Scatterplot

A graph that shows the relationship between two quantitative variables measured on the same individuals.

Explanatory Variable

The variable plotted on the horizontal axis (x-axis) of a scatterplot.

Response Variable

The variable plotted on the vertical axis (y-axis) of a scatterplot.

Girth

The circumference of a tree measured at a specific height above the ground.

Positive Association

A relationship where above-average values of one variable tend to accompany above-average values of the other.

Negative Association

A relationship where above-average values of one variable tend to accompany below-average values of the other.

Outlier

A data point that deviates significantly from the overall pattern in a scatterplot.

Linear Relationship

A relationship depicted as a straight line on a scatterplot.

Nonlinear Relationship

A relationship that cannot be represented as a straight line on a scatterplot.

Categorical Variable

A variable that can be divided into distinct categories, used in scatterplots with different colors or symbols.

Petal Length

A quantitative measurement representing the length of a flower petal, used in examples like the Iris dataset.

Petal Width

A quantitative measurement representing the width of a flower petal, used in examples like the Iris dataset.

Correlation

A statistic that measures the strength and direction of a linear relationship between two quantitative variables.

Pearson product-moment correlation coefficient

A measure that quantifies the direction and strength of the linear relationship between two quantitative variables.

r

The correlation coefficient, which ranges from -1 to 1, indicating the strength and direction of a linear relationship.

Outliers

Extreme values in data that can strongly affect the correlation coefficient.

Linear relationship

The relationship between two variables that can be represented by a straight line.

Explanatory variable

The independent variable in a study, which is manipulated to observe effects on a dependent variable.

Scatterplot

A graphical representation of the relationship between two quantitative variables, showing individual data points on a coordinate system.

Negative association

A situation in which the values of one variable decrease as the values of another variable increase, represented by a correlation coefficient less than zero.

Positive association

A situation in which the values of one variable increase as the values of another variable increase, represented by a correlation coefficient greater than zero.

r² (r squared)

The square of the correlation coefficient, representing the proportion of variation explained by the linear relationship between two variables.

Regression Line

A straight line that describes the relationship between a response variable y and an explanatory variable x.

Least-Squares Regression Line

The line that minimizes the sum of squares of the vertical distances from the data points to the line.

Slope

The amount by which the response variable y changes when the explanatory variable x increases by one unit.

Intercept

The value of the response variable y when the explanatory variable x equals zero.

Extrapolation

The use of a regression line for prediction beyond the range of the explanatory variable values used to create the line.

Multiple R-squared

The fraction of the variation in the response variable y explained by the least-squares regression of y on the explanatory variable x.

Residuals

The differences between the observed values and the values predicted by the regression model.

Prediction Equation

An equation derived from statistical output for predicting values of the response variable based on the explanatory variable.

Regression

A statistical method used to determine the relationship between variables, particularly how one variable affects another.

Residuals

The difference between an observed value and the value predicted by the regression line.

Residual Plot

A scatterplot of the regression residuals against the explanatory variable, used to assess the fit of a regression line.

Outlier

An observation that lies outside the overall pattern of the other observations in a data set.

Influential Observation

An observation that has a significant impact on the result of a statistical analysis when removed.

Lurking Variable

A variable that is not included among the explanatory or response variables in a study but may still influence the interpretation of relationships.

Correlation

A statistical measure that describes the extent to which two variables change in relation to each other.

Association Does Not Imply Causation

The principle that correlation between two variables does not necessarily mean that one causes the other.

Least-Squares Residuals

The differences between observed and predicted values in regression analysis that are minimized in the least-squares method.

Explanatory Variable

The variable that is manipulated or considered in a study to examine its effect on the response variable.

Two-Way Table

A statistical method used to summarize categorical data for two variables.

Simpson's Paradox

A phenomenon where a trend appears in several groups of data but disappears or reverses when these groups are combined.

Lurking Variable

A variable that is not included in the analysis but can influence the relationship between the studied variables.

Aggregation

The process of combining data from multiple sources or categories into a summary.

Categorical Data Analysis

A subfield of statistics that focuses on analyzing categorical data.

On-Time Arrival Rate

The percentage of flights that arrive on time relative to total flights.

Statistical Analysis

The process of collecting and examining data to discover patterns and draw conclusions.

Correlation Coefficient (r)

A statistical measure that describes the strength and direction of a relationship between two variables.

Intercept

The expected value of the dependent variable when all independent variable values are zero.

Slope

The rate of change in the dependent variable for every unit increase in the independent variable.

Causation

A relationship where a change in one variable causes a change in another variable.

Common Response

A situation where a lurking variable causes changes in both of the variables being studied.

Confounding

A situation where two variables both affect a third variable, making their individual effects indistinguishable.

Establishing Causation

Determining cause and effect typically done through experiments that change one explanatory variable while controlling other influences.

Association Consistency

In establishing causation, showing that a strong association is consistent across different regions or groups.

Alleged Cause Precedence

The principle that the alleged cause must precede the effect in time.

Plausibility of Cause

The idea that the proposed cause should be plausible, supported by existing research or experiments.

Example of Causation

An example is the relationship between the amount of fertilizer and the yield of crops.

Example of Common Response

An example is that nations with more TV sets have higher life expectancy due to wealth.

Example of Confounding

An example is both wealth and education affecting health outcomes.