st: RE: Matrix question- square roots of matrix elements

[Kit Baum <baum@bc.edu>]

clear
qui {
input y x1 x2 x3
123.1	1	1.92	12.4
124.3	1	2.15	9.9
89.3	1	1.67	2.4
141.3	1	1.68	13.8
112.8	1	1.75	3.5
108.1	1	1.55	1.8
143.9	1	1.54	17.8
124.2	1	2.1	9.8
110.1	1	2.44	8.3
111.7	1	2.47	9.8
123.8	1	1.86	12.6
123.5	1	1.93	11.5
110.2	1	2.47	7.4
100.9	1	2.11	6.1
123.3	1	2.1	9.5
115.7	1	1.73	8.8
116.6	1	1.86	4.9
153.5	1	2.19	18.8
149.2	1	1.9	18.9
89	1	1.67	2.3
132.6	1	2.43	14.1
97.5	1	2.13	2.9
106.1	1	2.33	5.9
115.3	1	1.75	7.6
98.5	1	2.05	5.3
135.1	1	2.35	16.8
124.2	1	2.12	8.8
98.4	1	2.13	3.2
114.8	1	1.89	5.4
142.5	1	1.5	17.3
122.6	1	1.93	11.2
127.7	1	2.27	11.2
113	1	1.66	7.9
144.2	1	1.73	17
109.2	1	1.59	3.3
106.8	1	2.29	7.1
145	1	1.86	15.3
124	1	1.91	12.7
106.7	1	2.34	6.1
153.2	1	2.13	19.6
120.1	1	2.05	6.3
119.3	1	1.89	9
150.6	1	2.12	18.7
92.2	1	1.87	2.2
130.5	1	2.09	16
112.5	1	1.76	4.5
111.8	1	1.77	4.3
120.1	1	1.94	9.3
107.4	1	2.37	8.3
128.6	1	2.1	15.4
124.6	1	2.29	9.2
127.2	1	2.36	10.2
end
}
mata:
st_view(y=.,.,"y")
st_view(X=.,.,("x1", "x2" ,"x3"))
b = invsym(X' * X) * (X' * y)
ehat = y - X * b
sigma = sqrt((ehat' * ehat)/(rows(X)-rows(b)))
se = diagonal(sqrt((sigma^2)*invsym(X' * X)))
t = b :/ se
bse = b,se,t
bse
cp = corr(variance((y,X * b),1))
r2 = cp[2,1]^2
bse
sigma
r2
end

regress y x2 x3


Note that r^2 can always be expressed as the square of the  
correlation of y, yhat.


Kit Baum, Boston College Economics
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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