［R］平均勤続年数と所定内賃金（「線形回帰分析」（朝倉書店）pp.116-118）

lm関数を使って計算している。以下に表示している表3.4（p.116）の値をCSV形式で入力したtable3_4.csvをカレントディレクトリに置いておくこと。

 i,     W, YEAR, DX
 1, 209.0,  0.3,  1
 2, 237.0,  2.0,  1
 3, 301.7,  5.9,  1
 4, 371.6, 10.1,  1
 5, 455.3, 14.9,  1
 6, 526.6, 20.9,  1
 7, 579.9, 25.4,  1
 8, 587.3, 29.3,  1
 9, 477.0, 33.8,  1
10, 201.7,  0.3,  0
11, 228.7,  2.6,  0
12, 271.5,  6.3,  0
13, 308.1,  9.8,  0
14, 342.7, 14.5,  0
15, 389.0, 20.0,  0
16, 394.6, 23.8,  0
17, 399.8, 28.3,  0
18, 317.0, 32.6,  0

実行してみる。

> dtf <- read.csv("table3_4.csv", header = TRUE)
> xx1i <- as.double(dtf$YEAR)
> xx2i <- as.double(dtf$DX)
> yyi <- as.double(dtf$W)
> r <- lm(yyi ~ 1 + log(xx1i) + I(xx1i ^ 2) + I(xx1i ^ 4) + I(xx2i * xx1i))
> print(summary(r))
Call:
lm(formula = yyi ~ 1 + log(xx1i) + I(xx1i^2) + I(xx1i^4) + I(xx2i * 
    xx1i))
Residuals:
    Min      1Q  Median      3Q     Max 
-17.136  -7.683   2.097   7.070  17.824 
Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     2.196e+02  4.748e+00   46.26 8.20e-16 ***
log(xx1i)       1.469e+01  3.257e+00    4.51 0.000586 ***
I(xx1i^2)       5.088e-01  3.531e-02   14.41 2.27e-09 ***
I(xx1i^4)      -4.446e-04  2.817e-05  -15.78 7.36e-10 ***
I(xx2i * xx1i)  6.523e+00  2.722e-01   23.96 3.84e-12 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 11.01 on 13 degrees of freedom
Multiple R-squared:  0.9937,    Adjusted R-squared:  0.9917 
F-statistic: 511.7 on 4 and 13 DF,  p-value: 3.746e-14
> yyhi <- r$fitted.value
> ei <- yyi - yyhi
> ri <- ei / yyi * 100
> ai2 <- ei ^ 2 / sum(ei ^ 2) * 100
> dtf <- data.frame(yyi, xx1i, yyhi, ei, ri, ai2)
> names(dtf) <- c("W", "YEAR", "Wの推定値", "残差", "誤差率", "平方残差率")
> print(dtf)
       W YEAR Wの推定値        残差     誤差率   平方残差率
1  209.0  0.3  203.9620   5.0379825  2.4105179  1.609669358
2  237.0  2.0  244.9042  -7.9041701 -3.3350929  3.962195699
3  301.7  5.9  301.3806   0.3194241  0.1058747  0.006470811
4  371.6 10.1  366.7761   4.8238794  1.2981376  1.475761750
5  455.3 14.9  447.5628   7.7372332  1.6993704  3.796599095
6  526.6 20.9  538.0347 -11.4347032 -2.1714210  8.292264754
7  579.9 25.4  576.0246   3.8753715  0.6682827  0.952467251
8  587.3 29.3  569.4762  17.8237961  3.0348708 20.147621237
9  477.0 33.8  492.7775 -15.7775142 -3.3076550 15.787033282
10 201.7  0.3  202.0051  -0.3050563 -0.1512426  0.005901786
11 228.7  2.6  237.1031  -8.4031158 -3.6742964  4.478205967
12 271.5  6.3  266.1784   5.3215546  1.9600569  1.795975490
13 308.1  9.8  297.9372  10.1627947  3.2985377  6.550126198
14 342.7 14.5  346.2444  -3.5444215 -1.0342636  0.796735341
15 389.0 20.0  396.0212  -7.0212080 -1.8049378  3.126418007
16 394.6 23.8  411.7361 -17.1361000 -4.3426508 18.622901255
17 399.8 28.3  391.0281   8.7718944  2.1940706  4.879891365
18 317.0 32.6  309.3476   7.6523586  2.4139932  3.713761354