The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

204
Part One
Single-Equation Regression Models
EXAMPLE 7.2
Coffee
Consumption in
the United States,
1970–1980
Consider the data in Table 7.1. The data pertain to consumption of cups of coffee per day
(
Y
) and real retail price of coffee (
X
) in the United States for years 1970–1980. Applying
OLS to the data, we obtain the following regression results:
ˆ
Y
t
=
2.6911
−
0.4795
X
t
(7.8.8)
se
=
(0.1216)
(0.1140)
RSS
=
0.1491; 
r
2
=
0.6628
The results make economic sense: As the price of coffee increases, on average, coffee con-
sumption goes down by about half a cup per day. The 
r
2
value of about 0.66 means that
the price of coffee explains about 66 percent of the variation in coffee consumption. The
reader can readily verify that the slope coefficient is statistically significant.
From the same data, the following double-log, or constant elasticity, model can be
estimated:
ln
Y
t
=
0.7774
−
0.2530 ln
X
t
(7.8.9)
se
=
(0.0152)
(0.0494)
RSS
=
0.0226;
r
2
=
0.7448
Since this is a double-log model, the slope coefficient gives a direct estimate of the price
elasticity coefficient. In the present instance, it tells us that if the price of coffee per pound
goes up by 1 percent, on average, per day coffee consumption goes down by about
0.25 percent. Remember that in the linear model (7.8.8) the slope coefficient only gives
the rate of change of coffee consumption with respect to price. (How will you estimate the
price elasticity for the linear model?) The 
r
2
value of about 0.74 means that about 74 per-
cent of the variation in the log of coffee demand is explained by the variation in the log of
coffee price.
Since the 
r
2
value of the linear model of 0.6628 is smaller than the 
r
2
value of 0.7448
of the log–linear model, you might be tempted to choose the latter model because of its