Regression Analysis and Correlation

These flashcards cover key concepts related to regression analysis and correlation as outlined in the lecture notes.

What is the purpose of the coefficient of determination (R²)?

R² measures the proportion of variance in the dependent variable that can be explained by the independent variable.

What indicates a high-leverage point in regression analysis?

A high-leverage point has a substantially larger or smaller x-value than other observations.

What does a positive residual indicate?

It indicates that the model underestimates the observed value.

What is the effect of removing a point with high influence from a regression analysis?

It can significantly change the slope, y-intercept, and correlation of the regression model.

What is a residual plot used for?

To check for the presence of patterns in residuals to determine if a linear model is appropriate.

Why are units important when interpreting slope in regression?

Slope is expressed in y-units per x-units and reflects how the y-variable changes with a one-unit change in the x-variable.

What does a higher R² value indicate?

It indicates a better fit of the linear model to the data.

How is the residual calculated?

Residual is calculated as the observed value minus the predicted value.

What does it mean if a scatterplot shows a linear association between two variables?

It suggests that predictions based on a linear model may be valid.

What does extrapolation refer to in the context of regression?

Extrapolation refers to making predictions beyond the observed range of data.