Applied Statistics Using SPSS, STATISTICA, MATLAB and R

278 7 Data Regression
Next, we create the X matrix by binding a column of ones, corresponding to the
intercept term in equation 7.1, to the PRT vector:
>> X = [PRT ones(size(PRT,1),1)]
We are now ready to apply the regress function:
>> [b,bint,r,rint,stats] = regress(ART,X,0.05);
The values of b, bint and stats are as follows:
>> b
b =
0.5469
-64.4902
>> bint
bint =
0.5294 0.5644
-78.4285 -50.5519
>> stats
stats =
1.0e+003 *
0.0010 3.8135 0
The values of b coincide with those in Figure 7.3. The intercept coefficient is
here the second element of b in correspondence with the (second) column of ones
of X. The values of bint are the 95% confidence intervals of b agreeing with the
values computed in Example 7.2 and Example 7.4, respectively. Finally, the first
value of stats is the R-square statistic; the second and third values are
respectively the ANOVA F and p discussed in section 7.1.4 and reported in Table
7.1. The exact value of the R-square statistic (without the four-digit rounding effect
of the above representation) can be obtained by previously issuing the format
long command.
Let us now illustrate the use of the R lm function for the same problem as in
Example 7.1. We have already used the lm function in Chapter 4 when computing
the ANOVA tests (see Commands 4.5 and 4.6). This function fits a linear model
describing the y data as a function of the X data. In chapter 4 the X data was a
categorical data vector (an R factor). Here, the X data correspond to the real-valued
predictors. Using the cork data frame we may run the lm function as follows:
> load(“e:cork”)
> attach(cork)
> summary(lm(ART~PRT))
Call:
lm(formula = ART ~ PRT)
Residuals:
Min 1Q Median 3Q Max
-95.651 -22.727 -1.016 19.012 152.143