Statistical Reasoning - Regression, Prediction, and Causation

These flashcards cover key concepts related to statistical reasoning, regression analysis, prediction, and causation, ensuring a comprehensive review for the exam.

What does a regression line describe?

It describes the relationship between an explanatory variable and a response variable.

What is the purpose of a regression line in statistical analysis?

To predict the value of a response variable y for a given value of an explanatory variable x.

In the context of fossil bones, how can you predict the length of the humerus from the femur?

Using the regression equation based on the lengths of the femur and humerus.

What happens when data points are more scattered in a regression analysis?

It leads to a weaker correlation and less accurate predictions.

What is the least-squares method in linear regression?

It minimizes the sum of squared errors for all predictions of y.

What do the coefficients a and b represent in the linear regression equation y = a + bx?

a is the intercept and b is the slope of the line.

What does R-squared (r2) represent in regression analysis?

It measures the proportion of the variation in the values of y that is explained by the regression on x.

What factor can significantly affect correlation and regression results?

Outliers can have a substantial impact on both correlation and regression.

What evidence supports a causal relationship in non-experimental studies?

Strong associations, consistency across studies, and dose-response relationships.

Why is it challenging to establish causation in statistical analysis?

There are many factors that can influence y, making it difficult to isolate the effect of a particular x-variable.