Linear Regression: Overview and Key Concepts

These flashcards cover foundational concepts of linear regression, including definitions, key formulas, and implications of R squared and p-values.

What is the first step in linear regression?

Use least squares to fit a line to the data.

What does R squared indicate in linear regression?

R squared indicates how much of the variation in the dependent variable can be explained by the independent variable.

What are residuals in the context of linear regression?

Residuals are the distances from the line to the data points.

What is the formula for R squared?

R squared = (Variation around the mean - Variation around the fit) / Variation around the mean.

If R squared equals 0.6, what does that mean about the variation?

It means that 60% of the variation in the dependent variable is explained by the independent variable.

What happens to R squared if you fit a plane instead of a line in linear regression?

You will fit a multiple regression model involving additional parameters, which could explain more variation.

What does a p-value indicate in the context of R squared?

The p-value indicates the statistical significance of the R squared value.

Why is it important to calculate an adjusted R squared?

Adjusted R squared accounts for the number of parameters in the model, preventing misleadingly high values from having too few data points.

In the context of multiple regression, what does the term 'overfitting' refer to?

Overfitting refers to a model that is too complex and captures noise in the data, leading to poor predictive performance.

What is the relationship between the number of data points and the p-value?

As the number of data points increases relative to the number of parameters, the p-value tends to decrease.