Lecture 6 Scatterplots and Regression_new

Bivariate Analysis

A statistical analysis that considers the relationship between two variables.

Scatterplot

A graphical representation that shows the relationship between two numerical variables measured on the same individuals.

Response Variable

The dependent variable that measures an outcome of a study.

Explanatory Variable

The independent variable that may explain or influence changes in a response variable.

Form

The overall shape of the relationship in a scatterplot, which can be linear, nonlinear, or show no association.

Strength

The closeness of the points in a scatterplot to a clear form, indicating the strength of the relationship.

Direction

The nature of the relationship between two variables, which can be positive or negative.

Correlation

The quantification of the degree to which two random variables are related.

Pearson’s Correlation Coefficient (r)

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

Outlier

An observation that lies an abnormal distance from other values in a dataset.

Influential Observation

An observation that significantly affects the result of a statistical calculation if removed.

Regression Line

A straight line that summarizes the linear relationship between two variables, used for prediction.

Slope

The estimated change in the response variable for every one unit increase in the explanatory variable.

Intercept

The estimated value of the response variable when the explanatory variable equals zero.

High Leverage

Outliers in the X direction that tend to have more effect on the correlation coefficient and regression equation.

Linear Relationship

A relationship that can be represented by a straight line in a scatterplot.

Nonexercise Activity (NEA)

Activities such as fidgeting or daily chores that are not deliberate exercise but can influence energy expenditure.

Moderate Correlation

A correlation coefficient (|r|) between 0.6 and 0.75 indicating a moderate strength of association.

Strong Correlation

A correlation coefficient (|r|) greater than 0.85 indicating a strong strength of association.

Bivariate Analysis

A bivariate analysis examines the relationship between ______ variables.

Statistical Relationships

Statistical relationships indicate overall tendencies, not ______ rules.

Scatterplots

Scatterplots are the best graphical representation for relationships between two ______ variables.

Axes

One variable is plotted on the horizontal (x) axis and the other on the vertical (y) ______.

Response Variable

The response variable is the dependent variable measuring the ______.

Explanatory Variable

The explanatory variable is the independent variable that may influence the ______ variable.

Form

The form of a scatterplot can be linear, nonlinear, or no ______.

Strength

The proximity of points to a clear form indicates ______.

Positive Association

A positive association means high values of one variable accompany high values of the ______.

Negative Association

A negative association means high values of one variable accompany low values of the ______.

NEA

NEA stands for nonexercise ______ activity.

Correlation Analysis

Correlation analysis quantifies the degree of ______ between two random variables.

Paired Data

Paired data means each variable is measured on the same ______.

Pearson’s Correlation Coefficient

Denoted as r, it measures the direction and strength of the ______ relationship.

Range

The range of r values is between ______ and 1.

Weak Linear Relationship

A value near 0 indicates a ______ linear relationship.

Strong Correlation

Strong correlation is defined as (0.85 < |r| ≤ ______).

Unitless

Correlation is ______, meaning it has no unit of measurement.

Sensitivity

Correlation is affected by ______.

Linear Regression

The purpose of linear regression is to summarize linear relationships in ______.

Regression Line

The regression line represents the relationship between explanatory and ______ variables.

Slope Interpretation

The slope represents the estimated change in the response variable for each unit ______ in the explanatory variable.

Intercept Interpretation

The intercept is the estimated value of the response variable when the explanatory variable equals ______.

High Leverage Points

High leverage points can significantly affect the regression ______.

Influential Observations

Influential observations are those whose removal can markedly change the ______.