Information Technology Reference
In-Depth Information
The righthand panel of
Figure 1-6
shows a histogram for the same data, but with more
bins and with replacements for the default title and
x
-axis label. It was created like this:
>
hist(Cars93$MPG.city, 20, main="City MPG (1993)", xlab="MPG")
See Also
The
histogram
function of the
lattice
package is an alternative to
hist
.
1.20 Performing Simple Linear Regression
Problem
You have two vectors,
x
and
y
, that hold paired observations: (
x
1
,
y
1
), (
x
2
,
y
2
), ..., (
x
n
,
y
n
). You believe there is a linear relationship between
x
and
y
, and you want to create
a regression model of the relationship.
Solution
The
lm
function performs a linear regression and reports the coefficients:
>
lm(y ~ x)
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
17.72 3.25
Discussion
Simple linear regression
involves two variables: a
predictor variable
, often called
x
; and
a
response variable
, often called
y
. The regression uses the ordinary least-squares (OLS)
algorithm to fit the linear model:
y
i
=
β
0
+
β
1
x
i
+
ε
i
where
β
0
and
β
1
are the regression coefficients and
ε
i
represents the error terms.
The
lm
function can perform linear regression. The main argument is a
model formu-
la
, such as
y ~ x
. The formula has the response variable on the left of the tilde character
(
~
) and the predictor variable on the right. The function estimates the regression coef-
ficients,
β
0
and
β
1
, and reports them as the intercept and the coefficient of
x
,
respectively:
Coefficients:
(Intercept) x
17.72 3.25
