why do residuals differ

Question

if we have

    dd <- structure(list(x = c(-0.27461139896373, -0.36715415967394, -0.396878987664827, 
-0.46247810661517, -0.348554552166752, -0.312871287128712, -0.305359246171965, 
-0.297850026219192, -0.38399462004035, -0.442901234567901, -0.436306074264866, 
-0.316390041493775), y = c(0.805840995132504, 1.9359410430839, 
0.820987654320988, 1.4328231292517, 0.91156462585034, 1.75308641975309, 
1.15646258503401, 1.42795138888889, 1.25575279421433, 3.13271604938272, 
0.825788751714678, 0.583974649162517), x2 = c(6.75, 4, 7.75, 
6.5, 5.33333333333333, 5.41666666666667, 5.16666666666667, 4.16666666666667, 
4.08333333333333, 2.83333333333333, 5.91666666666667, 5.75), 
    g = c("a1", "a3", "a5", "a6", "a2", "a1", "a2", "a1", "a2", 
    "a1", "a3", "a4")), .Names = c("x", "y", "x2", "g"), class = "data.frame", row.names = c(NA, 
-12L))

and do the model:

mm <- lm(y ~ x + x2 + g, 
              data = dd)
summary(mm)

we can get residuals in two ways:

res <- residuals(mm,type="partial")
partial.residuals <- resid(mm) + mm$coefficients["x"] * dd$x

why do these results differ?

res[,1]
partial.residuals

I want to plot the partial residuals of y on x

`lm` throws an error due to only one level existing for `g`. — jbaums, Sep 20 '14 at 13:30
By how much do they differ? Please post *your* results so we can verify it's not just floating-point rounding. — Carl Witthoft, Sep 20 '14 at 14:10

score 4 · Answer 1 · answered Sep 20 '14 at 14:47

The columns of resid(mm, type='partial') are equivalent to the working residuals (i.e. mm$residuals) plus the model coefficients multiplied by the respective centred regressors.

For example:

mm <- lm(y ~ x + x2 + g, data=dd)
residuals(mm,type="partial")
         x           x2           g
# 1  -0.18983646 -0.611273231  0.31089856
# 2   0.23116764  0.790012984  0.01595798
# 3   0.08354355 -1.069032332  0.46956893
# 4   0.24117753 -0.522368071  0.37710616
# 5  -0.02863590 -0.008204446 -0.38061524
# 6   0.17430042  0.244034093  0.58309734
# 7   0.14337349  0.340491370 -0.10480799
# 8  -0.69749887 -0.045005009 -0.25260602
# 9  -0.23111199  0.250821620 -0.66825343
# 10  0.42415724  1.311203154  0.52049360
# 11 -0.04076612 -0.486310617 -0.42214709
# 12 -0.10987052 -0.194369515 -0.44869282
# attr(,"constant")
# [1] 1.336908

resid(mm) + mm$coefficients['x'] * (dd$x - mean(dd$x))

#           1           2           3           4           5           6           7 
# -0.18983646  0.23116764  0.08354355  0.24117753 -0.02863590  0.17430042  0.14337349 
#           8           9          10          11          12 
# -0.69749887 -0.23111199  0.42415724 -0.04076612 -0.10987052 

resid(mm) + mm$coefficients['x2'] * (dd$x2 - mean(dd$x2))

#            1            2            3            4            5            6 
# -0.611273231  0.790012984 -1.069032332 -0.522368071 -0.008204446  0.244034093 
#            7            8            9           10           11           12 
#  0.340491370 -0.045005009  0.250821620  1.311203154 -0.486310617 -0.194369515

why do residuals differ

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