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4.1 The Linear Regression Model 159

Terminology for the Linear Regression Model Key Concept
with a Single Regressor
4.1
The linear regression model is

Yi = b0 + b1Xi + ui,

where

the subscript i runs over observations, i = 1, c, n;
Yi is the dependent variable, the regressand, or simply the left-hand variable;
Xi is the independent variable, the regressor, or simply the right-hand variable;
b0 + b1X is the population regression line or the population regression function;
b0 is the intercept of the population regression line;
b1 is the slope of the population regression line; and
ui is the error term.

Figure 4.1 Scatterplot of Test Score vs. Student–Teacher Ratio
(Hypothetical Data)

The scatterplot shows Test score (Y )

hypothetical observations 700

for seven school districts.

The population regres- 680 (X 1, Y1)

sion line is b0 + b1X. The u1 u2
vertical distance from the (X 2, Y2)

ith point to the population 660
regression line is

Yi - (b0 + b1Xi), which 640 b0 + b1X
is the population error

term ui for the ith 620
observation.

600
10 15 20 25 30
Student–teacher ratio (X )