What is the mathematical formula for the simple linear regression?

• A. y = x^2 + b
• B. y = a + b x^2
• C. y = b x + c
• D. y = mx + b

Answer: (D)

Simple linear regression describes a straight-line relationship between a single predictor x and the outcome y. The line is defined by a slope and an intercept: as x increases by one unit, y changes by a constant amount, and when x is zero, the predicted y is the intercept. The standard way to write this relationship is y = m x + b, with m as the slope and b as the intercept. This form is the conventional slope-intercept representation used in regression, directly capturing the idea of a linear relationship with one predictor.

The other forms don't fit the idea of a simple linear relationship: including x squared makes the relationship nonlinear, and while y = b x + c is a straight line, it uses nonstandard parameter labels compared to the typical regression notation (slope and intercept).