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--- multicolinearity [2018/12/26 02:41] – hkimscil
+++ multicolinearity [2018/12/26 02:49] (current) – [regression test with factors] hkimscil
@@ Line 24: / Line 24: @@
  $ sector    : int  1 1 1 0 0 0 0 0 1 0 ...
  $ marr      : int  1 1 0 0 1 0 0 0 1 0 ...
+> head(cps)
 > head(cps)
   education south sex experience union  wage age race occupation sector marr
@@ Line 34: / Line 34: @@
         13     0   0          9     1 13.07  28    3          6      0    0
 </code>
-<code>
-> cps$sex <- factor(cps$sex)
-> cps$union <- factor(cps$union)
-> cps$race <- factor(cps$race)
-> cps$sector <- factor(cps$sector)
-> cps$occupation <- factor(cps$occupation)
-> cps$marr <- factor(cps$marr)
-> str(cps)
-'data.frame':	534 obs. of  11 variables:
- $ education : int  8 9 12 12 12 13 10 12 16 12 ...
- $ south     : int  0 0 0 0 0 0 1 0 0 0 ...
- $ sex       : Factor w/ 2 levels "0","1": 2 2 1 1 1 1 1 1 1 1 ...
- $ experience: int  21 42 1 4 17 9 27 9 11 9 ...
- $ union     : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...
- $ wage      : num  5.1 4.95 6.67 4 7.5 ...
- $ age       : int  35 57 19 22 35 28 43 27 33 27 ...
- $ race      : Factor w/ 3 levels "1","2","3": 2 3 3 3 3 3 3 3 3 3 ...
- $ occupation: Factor w/ 6 levels "1","2","3","4",..: 6 6 6 6 6 6 6 6 6 6 ...
- $ sector    : Factor w/ 3 levels "0","1","2": 2 2 2 1 1 1 1 1 2 1 ...
- $ marr      : Factor w/ 2 levels "0","1": 2 2 1 1 2 1 1 1 2 1 ...
-> </code>
 <code>
@@ Line 67: / Line 44: @@
 Residuals:
      Min       1Q   Median       3Q      Max
--2.36167 -0.27926  0.00049  0.27957  1.79838
+-2.16246 -0.29163 -0.00469  0.29981  1.98248
 Coefficients:
-            Estimate Std. Error t value Pr(>|t|)
+             Estimate Std. Error t value Pr(>|t|)
-(Intercept)  1.54415    0.66955   2.306 0.021491 *
+(Intercept)  1.078596   0.687514   1.569 0.117291
-education    0.12525    0.10865   1.153 0.249530
+education    0.179366   0.110756   1.619 0.105949
-south       -0.09290    0.04197  -2.214 0.027291 *
+south       -0.102360   0.042823  -2.390 0.017187 *
-sex1        -0.21812    0.04193  -5.202 2.85e-07 ***
+sex         -0.221997   0.039907  -5.563 4.24e-08 ***
-experience   0.06799    0.10814   0.629 0.529813
+experience   0.095822   0.110799   0.865 0.387531
-union1       0.21178    0.05126   4.132 4.20e-05 ***
+union        0.200483   0.052475   3.821 0.000149 ***
-age         -0.05858    0.10806  -0.542 0.587963
+age         -0.085444   0.110730  -0.772 0.440671
-race2       -0.03345    0.09912  -0.338 0.735876
+race         0.050406   0.028531   1.767 0.077865 .
-race3        0.07973    0.05743   1.388 0.165636
+occupation  -0.007417   0.013109  -0.566 0.571761
-occupation2 -0.36440    0.09156  -3.980 7.88e-05 ***
+sector       0.091458   0.038736   2.361 0.018589 *
-occupation3 -0.20964    0.07624  -2.750 0.006171 **
+marr         0.076611   0.041931   1.827 0.068259 .
-occupation4 -0.38345    0.08105  -4.731 2.89e-06 ***
-occupation5 -0.05278    0.07287  -0.724 0.469223
-occupation6 -0.26555    0.08002  -3.318 0.000969 ***
-sector1      0.11532    0.05491   2.100 0.036186 *
-sector2      0.09296    0.09658   0.962 0.336262
-marr1        0.06335    0.04111   1.541 0.123899
 ---
 Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-Residual standard error: 0.4281 on 517 degrees of freedom
+Residual standard error: 0.4398 on 523 degrees of freedom
-Multiple R-squared:  0.3617,	Adjusted R-squared:  0.342
+Multiple R-squared:  0.3185,	Adjusted R-squared:  0.3054
-F-statistic: 18.31 on 16 and 517 DF,  p-value: < 2.2e-16
+F-statistic: 24.44 on 10 and 523 DF,  p-value: < 2.2e-16
->
 </code>
@@ Line 248: / Line 217: @@
 > </code>
+====== regression test with factors ======
 <code>
+> cps$sex <- factor(cps$sex)
+> cps$union <- factor(cps$union)
+> cps$race <- factor(cps$race)
+> cps$sector <- factor(cps$sector)
+> cps$occupation <- factor(cps$occupation)
+> cps$marr <- factor(cps$marr)
+> str(cps)
+'data.frame':	534 obs. of  11 variables:
+ $ education : int  8 9 12 12 12 13 10 12 16 12 ...
+ $ south     : int  0 0 0 0 0 0 1 0 0 0 ...
+ $ sex       : Factor w/ 2 levels "0","1": 2 2 1 1 1 1 1 1 1 1 ...
+ $ experience: int  21 42 1 4 17 9 27 9 11 9 ...
+ $ union     : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...
+ $ wage      : num  5.1 4.95 6.67 4 7.5 ...
+ $ age       : int  35 57 19 22 35 28 43 27 33 27 ...
+ $ race      : Factor w/ 3 levels "1","2","3": 2 3 3 3 3 3 3 3 3 3 ...
+ $ occupation: Factor w/ 6 levels "1","2","3","4",..: 6 6 6 6 6 6 6 6 6 6 ...
+ $ sector    : Factor w/ 3 levels "0","1","2": 2 2 2 1 1 1 1 1 2 1 ...
+ $ marr      : Factor w/ 2 levels "0","1": 2 2 1 1 2 1 1 1 2 1 ...
 </code>
 <code>
+> lm4 = lm(log(cps$wage) ~ . -age, data = cps)
+> summary(lm4)
+Call:
+lm(formula = log(cps$wage) ~ . - age, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.36103 -0.28080  0.00362  0.27793  1.79594
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  1.194821   0.181804   6.572 1.21e-10 ***
+education    0.066603   0.010060   6.621 8.96e-11 ***
+south       -0.093384   0.041931  -2.227  0.02637 *
+sex1        -0.216934   0.041844  -5.184 3.11e-07 ***
+experience   0.009371   0.001725   5.431 8.63e-08 ***
+union1       0.211506   0.051218   4.129 4.24e-05 ***
+race2       -0.033928   0.099051  -0.343  0.73209
+race3        0.079851   0.057392   1.391  0.16472
+occupation2 -0.364444   0.091500  -3.983 7.78e-05 ***
+occupation3 -0.210295   0.076175  -2.761  0.00597 **
+occupation4 -0.383882   0.080990  -4.740 2.77e-06 ***
+occupation5 -0.050664   0.072717  -0.697  0.48628
+occupation6 -0.265348   0.079969  -3.318  0.00097 ***
+sector1      0.114857   0.054862   2.094  0.03678 *
+sector2      0.093138   0.096514   0.965  0.33499
+marr1        0.062211   0.041025   1.516  0.13002
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4278 on 518 degrees of freedom
+Multiple R-squared:  0.3614,	Adjusted R-squared:  0.3429
+F-statistic: 19.54 on 15 and 518 DF,  p-value: < 2.2e-16
+>
 </code>
-<code>
+<code>> lm5 = lm(log(cps$wage) ~ . -age -race, data = cps)
+> summary(lm5)
+Call:
+lm(formula = log(cps$wage) ~ . - age - race, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.34366 -0.28169 -0.00017  0.29179  1.81158
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  1.224289   0.172070   7.115 3.73e-12 ***
+education    0.068838   0.009912   6.945 1.14e-11 ***
+south       -0.102588   0.041668  -2.462 0.014139 *
+sex1        -0.213602   0.041842  -5.105 4.65e-07 ***
+experience   0.009494   0.001723   5.510 5.65e-08 ***
+union1       0.202720   0.051009   3.974 8.06e-05 ***
+occupation2 -0.355381   0.091448  -3.886 0.000115 ***
+occupation3 -0.209820   0.076149  -2.755 0.006068 **
+occupation4 -0.385680   0.080855  -4.770 2.40e-06 ***
+occupation5 -0.047694   0.072746  -0.656 0.512351
+occupation6 -0.254277   0.079781  -3.187 0.001523 **
+sector1      0.111458   0.054845   2.032 0.042636 *
+sector2      0.099777   0.096481   1.034 0.301541
+marr1        0.065464   0.041036   1.595 0.111257
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4283 on 520 degrees of freedom
+Multiple R-squared:  0.3573,	Adjusted R-squared:  0.3412
+F-statistic: 22.24 on 13 and 520 DF,  p-value: < 2.2e-16
+>
 </code>
+<code>> lm6 = lm(log(cps$wage) ~ . -age -race -occupation -marr -sector, data = cps)
+> summary(lm6)
+Call:
+lm(formula = log(cps$wage) ~ . - age - race - occupation - marr -
+    sector, data = cps)
+Residuals:
+     Min       1Q   Median       3Q      Max
+-2.13809 -0.28681 -0.00078  0.29376  1.96678
+Coefficients:
+             Estimate Std. Error t value Pr(>|t|)
+(Intercept)  0.731792   0.122217   5.988 3.94e-09 ***
+education    0.094096   0.007942  11.848  < 2e-16 ***
+south       -0.111761   0.042857  -2.608 0.009372 **
+sex1        -0.231978   0.039202  -5.918 5.88e-09 ***
+experience   0.011548   0.001680   6.875 1.75e-11 ***
+union1       0.198360   0.051243   3.871 0.000122 ***
+---
+Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
+Residual standard error: 0.4433 on 528 degrees of freedom
+Multiple R-squared:  0.3011,	Adjusted R-squared:  0.2944
+F-statistic: 45.49 on 5 and 528 DF,  p-value: < 2.2e-16
+> </code>