In the regression model $Y \sim X$, to control for the effect of confounder $Z$ (where $X \leftarrow Z \rightarrow Y$) we can use the regression model $Y \sim X + Z$, i.e., taking the average effect of $X$ on $Y$ across differnt values of $Z$.

Deconfounding/Adjusting/Controlling a Measurable Confounder in a Regression Model

Regression model evaluation metrics are quantitative measures used to assess how well a model's predictions match the actual observed data. Common metrics include Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), the Coefficient of Determination ($$R^2$$), and Adjusted $$R^2$$.

Regression Model Evaluation Metrics

A regression model predicts a value $$Y$$ given a set of $$X$$ variables. In the regression model $$Y \sim X$$, we measure the effect of $$X$$ on $$Y$$, i.e., we measure the association between changes in values of $$X$$ and changes in values of $$Y$$. Analyzing a regression model is a method used to solve a regression problem.

Reference: James, G., Witten, D., Hastie, T., & Tibshirani, R. (2017). An introduction to statistical learning: with applications in R. New York: Springer.

Johns Hopkins University

University of Michigan - Ann Arbor

Google

- Regression Models
- Decision Tree Models
- Random Forest Models
- Support Vector Machine
- Naive Bayes
- K Means
- KNN

Classical SL Methods (examples)

A regression problem is a type of supervised machine learning task where the objective is to predict an unknown, continuous numerical label based on known input features. It is used to answer 'how much?' or 'how many?' questions. The defining characteristic is that the target labels take on arbitrary numerical values, and the goal of the learning algorithm is to produce a model whose predictions closely approximate these actual observed values.

Regression Problem

Regression Model

Predicting the height of a pediatric patient for a given year based on family trends and input data about the patient's current height/weight data.

Example of A Regression Problem

- Linear regression
- Nonlinear regression

Types of regression

https://towardsdatascience.com/regression-an-explanation-of-regression-metrics-and-what-can-go-wrong-a39a9793d914

Regression Metrics

What is the differnce between classification and regression?

https://beginningwithml.wordpress.com/2018/07/02/5-locally-weighted-linear-regression/
Locally weighted linear regression is a general linear regression method, it's also a local regression method. We can know more about local regression by checking its related wiki: https://en.wikipedia.org/wiki/Local_regression

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