The Linear Regression model assumes that there is a linear, or "straight line", relationship between the dependent variable and each predictor. This relationship is described in the following formula.
y = b_0 + b_1 x_1 + ... + b_p x_p + e
y is the response
b_j is the value of the jth regression coefficient
x_j is the jth predictor
e is the error term
The model is linear because increasing the value of the jth predictor by 1 unit increases the value of the dependent by bj units.
For the purposes of testing hypotheses about the values of model parameters, the linear regression model also assumes:
The error term has a normal distribution with mean 0.
The variance of the error term is constant across cases and independent of the variables in the model. An error term with non-constant variance is said to be heteroscedastic.
The value of the error term for a given case is independent of the values of the variables in the model and of the values of the error term for other cases.