Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

This section focuses on the key features and methods for working with linear graphs. It demonstrates how to sketch graphs from rules, derive rules from graphs, and calculate key features such as the ...

Apple improved the Math Notes feature in iOS 26 and iPadOS 26, allowing users to input equations to create graphs in three dimensions. With ‌iOS 26‌ and ‌iPadOS 26‌, when you write an equation with ...

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number ...

The word correlation is used in everyday life to denote some form of association. We might say that we have noticed a correlation between foggy days and attacks of wheeziness. However, in statistical ...

Simultaneous linear equations are used to model situations where two relationships must be satisfied at the same time. These problems often involve two interdependent variables, such as comparing ...

A general implementation of Structural Equation Models with latent variables (MLE, 2SLS, and composite likelihood estimators) with both continuous, censored, and ordinal outcomes (Holst and ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Graphing an equation is an essential skill in mathematics, as it helps us visualize the relationships between variables. There are several techniques that can be employed to make graphing easier and ...