Class Notes Ch. 3: Simple Linear Regression STAT 4230/6230
Ch. 3.2: The Simple linear regression model
The term 𝐸(𝑦) captures the model’s predictions, but since this is never perfect, we need to include
an error term 𝜀 which represents the random (i.e. cannot be predicted) variations of the observed
values of Y around their predicted values 𝐸(𝑦). This is the unexplained variation in 𝑌 that is due
to other factors not in the current model. A good model will have small errors, implying that most
of the variation in Y can be accounted for by 𝐸(𝑦).
The simplest model is a first-order linear model, which is just a straight line of 𝑌 vs. 𝑋:
• The slope gives the predicted increase in 𝑌 per unit of 𝑋, or the rate of change between 𝑌
and 𝑋. If the slope = 0 (line = horizontal), 𝑌 does not change in relation to 𝑋 and 𝑋 does
not help predict the value of 𝑌.
1
Ch. 3.2: The Simple linear regression model
The term 𝐸(𝑦) captures the model’s predictions, but since this is never perfect, we need to include
an error term 𝜀 which represents the random (i.e. cannot be predicted) variations of the observed
values of Y around their predicted values 𝐸(𝑦). This is the unexplained variation in 𝑌 that is due
to other factors not in the current model. A good model will have small errors, implying that most
of the variation in Y can be accounted for by 𝐸(𝑦).
The simplest model is a first-order linear model, which is just a straight line of 𝑌 vs. 𝑋:
• The slope gives the predicted increase in 𝑌 per unit of 𝑋, or the rate of change between 𝑌
and 𝑋. If the slope = 0 (line = horizontal), 𝑌 does not change in relation to 𝑋 and 𝑋 does
not help predict the value of 𝑌.
1
