The simple linear regression model
In Example 4.6.1. Resistant line for the IO-CPU time of Chapter 4, Exploratory Analysis, we built a resistant line for CPU_Time as a function of the No_of_IO processes. The results were satisfactory in the sense that the fitted line was very close to covering all the data points (refer to the Resistant line for CPU_Time figure of Chapter 4, Exploratory Analysis). However, we need more statistical validation of the estimated values of the slope and intercept terms. Here, we take a different approach and state the linear regression model in more technical details.
The simple linear regression model is given by 
, where X is the covariate/independent variable, Y is the regressand/dependent variable, and ε is the unobservable error term. The parameters of the linear model are specified by 
and 
. Here, is the intercept term and corresponds to the value of Y when x = 0. The slope term, , reflects the change in the Y value for a unit change in X. It is also common...
