Linear Regression Lecture Notes

These flashcards cover key concepts from the lecture on Linear Regression, focusing on the definitions and relationships important for understanding bivariate data and regression analysis.

Bivariate Data

Data involving two different quantitative variables, such as hours of sleep and test performance.

Response Variable (y)

The dependent variable that measures the outcome of a study.

Explanatory Variable (x)

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

Scatterplot

A graphical representation of the relationship between two quantitative variables by plotting pairs of observed values.

Positive Association

A relationship where an increase in the explanatory variable (x) results in an increase in the response variable (y).

Negative Association

A relationship where an increase in the explanatory variable (x) results in a decrease in the response variable (y).

Correlation Coefficient (r)

A numerical measurement of the strength and direction of the linear relationship between two quantitative variables.

Least Squares Regression Line

The line that minimizes the sum of the squared residuals between observed values and predicted values.

Residual

The difference between an observed value and the predicted value provided by a regression model.

Lurking Variable

A variable that is not included as an explanatory or response variable in a study but can influence the interpretation of the relationship.

Causation

The relationship where changes in one variable directly cause changes in another variable.

Intercept (b0)

The value of the response variable when the explanatory variable is zero.

Slope (b1)

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

Outlier

An observation that deviates significantly from the overall pattern of data in a scatterplot.

Linear Relationship

A relationship where the points in a scatterplot roughly follow a straight line.

Extrapolation

Using a regression model to predict values outside the range of observed data.