Which type of regression represents the following formula: y = c + b*x, where y = estimated dependent variable score, c = constant, b = regression coefficient, and x = score on the independent variable?

The formula y = c + bx represents a simple linear regression model. It describes a linear relationship between a single independent variable (x) and a dependent variable (y). The constant 'c' is the y-intercept (the value of y when x is 0), and 'b' is the regression coefficient, representing the slope of the line. This equation models how a change in the independent variable is predicted to affect the dependent variable. It is the foundational equation for predicting a continuous outcome based on a single predictor.

A. Lasso regression: This is a regularized linear model that adds a penalty term to the loss function; its formula is more complex and aims to perform feature selection.
C. Polynomial regression: This models a non-linear relationship using a polynomial function (e.g., y = c + b₁x + b₂x²), not a straight line.
D. Ridge regression: This is another regularized linear model that adds a different type of penalty term to prevent overfitting, but the base formula is not this simple.

1. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning: with Applications in R. Springer. In Chapter 3, "Linear Regression," the simple linear regression model is defined as Y ≈ β₀ + β₁X (p. 61, Equation 3.1), which is equivalent to the formula in the question.

2. MIT OpenCourseWare. (2016). 18.650 Statistics for Applications, Fall 2016. Massachusetts Institute of Technology. Lecture 15 notes introduce the simple linear regression model as Yi = a + bxi + εi, where the deterministic part is the line a + bx. (Section 15.2, p. 2).