## [1] "1. Leitura dos dados"
## [1] "2. Exploração inicial"
## Rows: 15,395
## Columns: 34
## $ ano <chr> "2016", "2016", "2016", "2016", "2016", "2016", "2016", "20…
## $ ponto <chr> "CF1658277", "CF1658272", "CF1658273", "CF1658274", "CF1658…
## $ x <dbl> -49.18157, -49.18953, -49.18786, -49.18619, -49.18453, -49.…
## $ y <dbl> -21.27265, -21.27243, -21.27241, -21.27239, -21.27237, -21.…
## $ variedade <chr> "CV6654", "CV6654", "CV6654", "CV6654", "CV6654", "CV6654",…
## $ solos <chr> "LVal md", "LVPd md/arg", "LVPd md/arg", "LVPd md/arg", "LV…
## $ tch_real <dbl> 63.54, 63.54, 63.54, 63.54, 63.54, 63.54, 63.54, 63.54, 63.…
## $ atr <dbl> 148.07, 148.07, 148.07, 148.07, 148.07, 148.07, 148.07, 148…
## $ ph_cacl2_1 <dbl> 5.19, 5.18, 4.88, 4.96, 5.05, 5.15, 6.24, 4.50, 5.38, 5.50,…
## $ mo_1 <dbl> 16.2022, 17.0236, 15.6546, 13.7380, 15.6546, 14.0118, 11.82…
## $ p_resina_1 <dbl> 11.538500, 12.526100, 10.880100, 10.715500, 11.044700, 11.2…
## $ s_1 <dbl> 8.84769, 9.92472, 12.07878, 8.96736, 9.56571, 8.01000, 9.80…
## $ ca_1 <dbl> 21.601449, 19.862319, 14.789855, 16.601449, 18.195652, 19.4…
## $ mg_1 <dbl> 11.045207, 15.713952, 5.495713, 9.696804, 10.047545, 10.359…
## $ k_1 <dbl> 1.2805516, 0.9239182, 1.4992867, 1.5563481, 1.6229196, 0.84…
## $ al_1 <dbl> 1.19600, 0.92000, 1.38000, 0.55200, 0.82800, 1.19600, 0.644…
## $ h_al_1 <dbl> 22.96210, 22.01502, 30.19345, 22.72158, 22.01502, 19.40179,…
## $ sb_1 <dbl> 33.92721, 36.50019, 21.78485, 27.85460, 29.86612, 30.63469,…
## $ ctc_1 <dbl> 56.88931, 58.51521, 51.97831, 50.57618, 51.88114, 50.03647,…
## $ v_1 <dbl> 59.63723, 62.37726, 41.91144, 55.07455, 57.56642, 61.22471,…
## $ m_1 <dbl> 3.4051560, 2.4585659, 5.9573004, 1.9432103, 2.6975854, 3.75…
## $ ph_cacl2_2 <dbl> 4.90, 5.38, 5.29, 5.30, 5.16, 5.06, 5.50, 4.50, 4.79, 4.46,…
## $ mo_2 <dbl> 13.7380, 13.4642, 12.3690, 11.5476, 13.7380, 11.5476, 11.82…
## $ p_resina_2 <dbl> 12.032300, 11.703100, 11.703100, 13.513700, 11.867700, 11.8…
## $ s_2 <dbl> 12.43779, 16.86558, 11.00175, 8.12967, 12.19845, 13.27548, …
## $ ca_2 <dbl> 14.210145, 16.021739, 15.514493, 14.427536, 15.224638, 14.5…
## $ mg_2 <dbl> 7.085737, 9.735776, 6.563523, 8.262666, 7.327358, 7.475448,…
## $ k_2 <dbl> 0.8050404, 0.7194484, 0.9429387, 0.5863053, 0.7669995, 0.67…
## $ al_2 <dbl> 3.956000, 1.012000, 1.104000, 0.736000, 2.024000, 2.852000,…
## $ h_al_2 <dbl> 43.19156, 26.60941, 24.98024, 21.33044, 24.71858, 26.33069,…
## $ sb_2 <dbl> 22.100922, 26.476963, 23.020954, 23.276507, 23.318995, 22.7…
## $ ctc_2 <dbl> 65.29248, 53.08638, 48.00119, 44.60695, 48.03757, 49.05050,…
## $ v_2 <dbl> 33.84911, 49.87525, 47.95913, 52.18135, 48.54324, 46.31922,…
## $ m_2 <dbl> 15.182146, 3.681478, 4.576174, 3.065069, 7.986428, 11.15290…
## [1] "3. Testes de normalidade"
## [1] "4. Estatística descritiva"
Estatística descritiva das variáveis (2016)
| Min |
30.2600000 |
98.2000000 |
3.8700000 |
5.640370 |
0.8850791 |
1.203450 |
2.924390 |
1.256037 |
0.0818452 |
0.0000000 |
6.698175 |
5.269530 |
23.767015 |
14.1289129 |
0.0000000 |
| Q1 |
67.3800000 |
125.3800000 |
5.3700000 |
10.980940 |
9.4110000 |
4.175940 |
17.217109 |
6.937585 |
1.2542336 |
0.2640000 |
12.806593 |
26.513523 |
42.126448 |
61.6581787 |
0.2634787 |
| Med |
80.7000000 |
134.0800000 |
5.6400000 |
12.864200 |
12.5864200 |
5.861650 |
21.211485 |
8.849670 |
2.0473583 |
0.4400000 |
14.911237 |
32.539437 |
48.260220 |
68.4931971 |
1.2034469 |
| Média |
82.8544152 |
133.2789225 |
5.6322684 |
13.245157 |
15.6960641 |
6.945619 |
21.947658 |
9.139075 |
2.4257255 |
0.7088048 |
15.709103 |
33.510965 |
49.218307 |
67.0083418 |
2.4824255 |
| Q3 |
100.2325000 |
142.3700000 |
5.9200000 |
15.000000 |
18.4697500 |
8.302680 |
25.537540 |
11.058157 |
3.0856830 |
0.7680000 |
17.726578 |
39.169895 |
54.679593 |
73.8494267 |
2.7150839 |
| Max |
148.2733333 |
163.9500000 |
6.9200000 |
41.570400 |
178.6540400 |
115.583760 |
222.901024 |
43.399123 |
16.1711794 |
28.0991300 |
57.394880 |
239.138509 |
250.125865 |
95.6072694 |
68.1282220 |
| DP |
21.6648083 |
11.0181877 |
0.4312539 |
3.213383 |
11.7458092 |
4.688293 |
8.245786 |
3.228851 |
1.6422119 |
1.1129639 |
4.162032 |
11.204547 |
10.933854 |
9.8480210 |
4.8277303 |
| CV |
26.1480432 |
8.2670144 |
7.6568424 |
24.260816 |
74.8328317 |
67.500006 |
37.570231 |
35.330171 |
67.6998227 |
157.0198106 |
26.494393 |
33.435465 |
22.215013 |
14.6967090 |
194.4763406 |
| Skn |
0.1389253 |
-0.3273455 |
-0.2799568 |
1.146322 |
4.8479280 |
6.651223 |
5.923979 |
1.045592 |
1.6595194 |
7.9888967 |
1.609074 |
3.169909 |
3.168654 |
-0.9762067 |
5.9547436 |
| Krt |
-0.5549391 |
-0.5471759 |
0.6023940 |
4.346268 |
44.3593044 |
111.231886 |
112.166201 |
5.725034 |
4.3361894 |
125.3526633 |
5.997423 |
40.817014 |
40.096410 |
1.8770659 |
49.9723231 |
## [1] "5. Transformações"
Estatística descritiva após transformações (2016)
| Min |
30.2600000 |
98.2000000 |
3.8700000 |
5.640370 |
0.6339698 |
0.1851924 |
1.0730860 |
1.256037 |
0.0818452 |
0.0000000 |
6.698175 |
1.6619412 |
3.1682987 |
14.1289129 |
0.0000000 |
| Q1 |
67.3800000 |
125.3800000 |
5.3700000 |
10.980940 |
2.3428629 |
1.4293395 |
2.8459036 |
6.937585 |
1.2542336 |
0.2640000 |
12.806593 |
3.2776549 |
3.7406758 |
61.6581787 |
0.2338688 |
| Med |
80.7000000 |
134.0800000 |
5.6400000 |
12.864200 |
2.6090708 |
1.7684311 |
3.0545428 |
8.849670 |
2.0473583 |
0.4400000 |
14.911237 |
3.4824528 |
3.8766076 |
68.4931971 |
0.7900229 |
| Média |
82.8544152 |
133.2789225 |
5.6322684 |
13.245157 |
2.6678794 |
1.7992253 |
3.0333194 |
9.139075 |
2.4257255 |
0.7088048 |
15.709103 |
3.4619190 |
3.8750668 |
67.0083418 |
0.8789997 |
| Q3 |
100.2325000 |
142.3700000 |
5.9200000 |
15.000000 |
2.9688620 |
2.1165784 |
3.2401495 |
11.058157 |
3.0856830 |
0.7680000 |
17.726578 |
3.6679085 |
4.0014906 |
73.8494267 |
1.3124013 |
| Max |
148.2733333 |
163.9500000 |
6.9200000 |
41.570400 |
5.1910330 |
4.7499955 |
5.4067278 |
43.399123 |
16.1711794 |
28.0991300 |
57.394880 |
5.4770429 |
5.5219642 |
95.6072694 |
4.2359631 |
| DP |
21.6648083 |
11.0181877 |
0.4312539 |
3.213383 |
0.5114056 |
0.5028749 |
0.3330605 |
3.228851 |
1.6422119 |
1.1129639 |
4.162032 |
0.3198412 |
0.2024683 |
9.8480210 |
0.7534231 |
| CV |
26.1480432 |
8.2670144 |
7.6568424 |
24.260816 |
19.1689932 |
27.9495228 |
10.9800672 |
35.330171 |
67.6998227 |
157.0198106 |
26.494393 |
9.2388412 |
5.2248985 |
14.6967090 |
85.7136922 |
| Skn |
0.1389253 |
-0.3273455 |
-0.2799568 |
1.146322 |
0.5613552 |
0.4610621 |
-0.2831555 |
1.045592 |
1.6595194 |
7.9888967 |
1.609074 |
-0.4055664 |
0.3573076 |
-0.9762067 |
0.9660524 |
| Krt |
-0.5549391 |
-0.5471759 |
0.6023940 |
4.346268 |
1.2338472 |
0.7120912 |
2.8079779 |
5.725034 |
4.3361894 |
125.3526633 |
5.997423 |
2.2820944 |
2.3775535 |
1.8770659 |
1.1918748 |
## [1] "6. Seleção de ano/variável"
## Rows: 3,703
## Columns: 3
## $ x <dbl> -49.29976, -49.29920, -49.29879, -49.29791, -49.29754, -49.29691, -4…
## $ y <dbl> -20.93966, -20.93773, -20.93591, -20.93728, -20.94069, -20.93094, -2…
## $ z <dbl> 78.34737, 78.34737, 78.44737, 78.44737, 78.34737, 99.51500, 102.6750…
## [1] "7. Boxplot / histograma / normalidade"
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 30.26 67.38 80.70 82.85 100.23 148.27
##
## Shapiro-Wilk normality test
##
## data: y_vals
## W = 0.99016, p-value = 2.374e-15
##
## Cramer-von Mises normality test
##
## data: y_vals
## W = 2.0064, p-value = 7.37e-10
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: y_vals
## D = 0.051527, p-value < 2.2e-16
##
## Anderson-Darling normality test
##
## data: y_vals
## A = 11.356, p-value < 2.2e-16
## [1] "8. Colinearidade"
## tch_real atr ph_cacl2_1 mo_1 p_resina_1 s_1 ca_1 mg_1 k_1
## tch_real 1.00 -0.08 0.00 -0.05 0.01 -0.09 -0.01 0.00 -0.09
## atr -0.08 1.00 -0.05 0.01 0.05 0.08 -0.03 0.00 0.04
## ph_cacl2_1 0.00 -0.05 1.00 0.07 0.28 -0.04 0.55 0.49 0.27
## mo_1 -0.05 0.01 0.07 1.00 0.11 0.13 0.31 0.30 0.19
## p_resina_1 0.01 0.05 0.28 0.11 1.00 -0.07 0.28 0.16 0.17
## s_1 -0.09 0.08 -0.04 0.13 -0.07 1.00 0.01 0.03 0.24
## ca_1 -0.01 -0.03 0.55 0.31 0.28 0.01 1.00 0.69 0.29
## mg_1 0.00 0.00 0.49 0.30 0.16 0.03 0.69 1.00 0.38
## k_1 -0.09 0.04 0.27 0.19 0.17 0.24 0.29 0.38 1.00
## al_1 -0.07 0.04 -0.41 -0.03 -0.18 0.16 -0.37 -0.23 -0.10
## h_al_1 -0.03 0.06 -0.58 0.11 -0.15 0.10 -0.30 -0.24 -0.12
## sb_1 -0.02 -0.01 0.59 0.33 0.27 0.06 0.96 0.83 0.46
## ctc_1 -0.04 0.01 0.33 0.41 0.21 0.11 0.85 0.77 0.44
## v_1 0.00 -0.04 0.73 0.16 0.27 -0.02 0.82 0.69 0.38
## m_1 -0.06 0.16 -0.55 -0.06 -0.24 0.16 -0.52 -0.38 -0.21
## al_1 h_al_1 sb_1 ctc_1 v_1 m_1
## tch_real -0.07 -0.03 -0.02 -0.04 0.00 -0.06
## atr 0.04 0.06 -0.01 0.01 -0.04 0.16
## ph_cacl2_1 -0.41 -0.58 0.59 0.33 0.73 -0.55
## mo_1 -0.03 0.11 0.33 0.41 0.16 -0.06
## p_resina_1 -0.18 -0.15 0.27 0.21 0.27 -0.24
## s_1 0.16 0.10 0.06 0.11 -0.02 0.16
## ca_1 -0.37 -0.30 0.96 0.85 0.82 -0.52
## mg_1 -0.23 -0.24 0.83 0.77 0.69 -0.38
## k_1 -0.10 -0.12 0.46 0.44 0.38 -0.21
## al_1 1.00 0.33 -0.36 -0.16 -0.44 0.75
## h_al_1 0.33 1.00 -0.30 0.14 -0.74 0.36
## sb_1 -0.36 -0.30 1.00 0.89 0.85 -0.53
## ctc_1 -0.16 0.14 0.89 1.00 0.53 -0.35
## v_1 -0.44 -0.74 0.85 0.53 1.00 -0.57
## m_1 0.75 0.36 -0.53 -0.35 -0.57 1.00
## ca_1 mg_1 h_al_1 sb_1 ctc_1 v_1
## 64.89353 12.33205 25.53703 225.53331 70.44043 112.30707
## [1] "9. Regressão múltipla e Stepwise"
##
## Call:
## lm(formula = form_reg, data = df_aux)
##
## Residuals:
## Min 1Q Median 3Q Max
## -65.387 -20.944 -4.705 20.946 120.330
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 168.85616 12.31080 13.716 < 2e-16 ***
## atr -0.19359 0.03289 -5.886 4.11e-09 ***
## ph_cacl2_1 -3.46843 1.01665 -3.412 0.000649 ***
## mo_1 -0.25834 0.11202 -2.306 0.021131 *
## p_resina_1 1.45841 0.69956 2.085 0.037125 *
## s_1 -2.87654 0.70160 -4.100 4.17e-05 ***
## mg_1 0.78110 0.17500 4.463 8.18e-06 ***
## k_1 -1.44046 0.23506 -6.128 9.32e-10 ***
## al_1 -1.61502 0.49033 -3.294 0.000993 ***
## ctc_1 -8.87523 2.85928 -3.104 0.001916 **
## m_1 -1.18414 0.79451 -1.490 0.136160
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.39 on 7950 degrees of freedom
## Multiple R-squared: 0.02705, Adjusted R-squared: 0.02582
## F-statistic: 22.1 on 10 and 7950 DF, p-value: < 2.2e-16
##
## studentized Breusch-Pagan test
##
## data: modelo_final
## BP = 117.94, df = 10, p-value < 2.2e-16
##
## Durbin-Watson test
##
## data: modelo_final
## DW = 1.3203, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0
## Start: AIC=54034.62
## tch_real ~ 1
##
## Df Sum of Sq RSS AIC
## + s_1 1 62103 6994503 53966
## + k_1 1 56291 7000315 53973
## + atr 1 43536 7013071 53987
## + al_1 1 38820 7017787 53993
## + m_1 1 27826 7028780 54005
## + mo_1 1 15442 7041164 54019
## + ctc_1 1 10310 7046296 54025
## <none> 7056607 54035
## + p_resina_1 1 1018 7055589 54035
## + mg_1 1 59 7056547 54037
## + ph_cacl2_1 1 3 7056603 54037
##
## Step: AIC=53966.25
## tch_real ~ s_1
##
## Df Sum of Sq RSS AIC
## + atr 1 36172 6958331 53927
## + k_1 1 33501 6961002 53930
## + al_1 1 25354 6969149 53939
## + m_1 1 16742 6977761 53949
## + mo_1 1 8698 6985805 53958
## + ctc_1 1 5526 6988977 53962
## <none> 6994503 53966
## + p_resina_1 1 235 6994268 53968
## + mg_1 1 202 6994301 53968
## + ph_cacl2_1 1 67 6994436 53968
##
## Step: AIC=53926.97
## tch_real ~ s_1 + atr
##
## Df Sum of Sq RSS AIC
## + k_1 1 32053 6926279 53892
## + al_1 1 23409 6934922 53902
## + m_1 1 10296 6948036 53917
## + mo_1 1 8570 6949762 53919
## + ctc_1 1 5395 6952936 53923
## <none> 6958331 53927
## + p_resina_1 1 674 6957658 53928
## + ph_cacl2_1 1 278 6958054 53929
## + mg_1 1 209 6958122 53929
##
## Step: AIC=53892.21
## tch_real ~ s_1 + atr + k_1
##
## Df Sum of Sq RSS AIC
## + al_1 1 33007 6893272 53856
## + m_1 1 24046 6902233 53867
## + mg_1 1 8080 6918199 53885
## + mo_1 1 4056 6922223 53890
## + p_resina_1 1 3756 6922523 53890
## <none> 6926279 53892
## + ph_cacl2_1 1 1285 6924994 53893
## + ctc_1 1 10 6926268 53894
##
## Step: AIC=53856.19
## tch_real ~ s_1 + atr + k_1 + al_1
##
## Df Sum of Sq RSS AIC
## + mo_1 1 4642.1 6888630 53853
## + mg_1 1 3107.8 6890164 53855
## <none> 6893272 53856
## + ph_cacl2_1 1 1442.3 6891830 53857
## + p_resina_1 1 1166.9 6892105 53857
## + m_1 1 833.3 6892439 53857
## + ctc_1 1 471.3 6892801 53858
##
## Step: AIC=53852.82
## tch_real ~ s_1 + atr + k_1 + al_1 + mo_1
##
## Df Sum of Sq RSS AIC
## + mg_1 1 5708.0 6882922 53848
## <none> 6888630 53853
## + p_resina_1 1 1655.2 6886975 53853
## + ph_cacl2_1 1 1329.0 6887301 53853
## + m_1 1 1002.3 6887628 53854
## + ctc_1 1 13.1 6888617 53855
##
## Step: AIC=53848.22
## tch_real ~ s_1 + atr + k_1 + al_1 + mo_1 + mg_1
##
## Df Sum of Sq RSS AIC
## + ph_cacl2_1 1 5338.3 6877584 53844
## + ctc_1 1 4762.9 6878159 53845
## <none> 6882922 53848
## + p_resina_1 1 1391.2 6881531 53849
## + m_1 1 106.4 6882816 53850
##
## Step: AIC=53844.05
## tch_real ~ s_1 + atr + k_1 + al_1 + mo_1 + mg_1 + ph_cacl2_1
##
## Df Sum of Sq RSS AIC
## + ctc_1 1 5824.2 6871760 53839
## + p_resina_1 1 2766.5 6874817 53843
## <none> 6877584 53844
## + m_1 1 1018.8 6876565 53845
##
## Step: AIC=53839.3
## tch_real ~ s_1 + atr + k_1 + al_1 + mo_1 + mg_1 + ph_cacl2_1 +
## ctc_1
##
## Df Sum of Sq RSS AIC
## + p_resina_1 1 4100.4 6867659 53837
## + m_1 1 2265.4 6869494 53839
## <none> 6871760 53839
##
## Step: AIC=53836.55
## tch_real ~ s_1 + atr + k_1 + al_1 + mo_1 + mg_1 + ph_cacl2_1 +
## ctc_1 + p_resina_1
##
## Df Sum of Sq RSS AIC
## + m_1 1 1918.3 6865741 53836
## <none> 6867659 53837
##
## Step: AIC=53836.33
## tch_real ~ s_1 + atr + k_1 + al_1 + mo_1 + mg_1 + ph_cacl2_1 +
## ctc_1 + p_resina_1 + m_1
##
## Call:
## lm(formula = tch_real ~ s_1 + atr + k_1 + al_1 + mo_1 + mg_1 +
## ph_cacl2_1 + ctc_1 + p_resina_1 + m_1, data = variaveis_validas)
##
## Residuals:
## Min 1Q Median 3Q Max
## -65.387 -20.944 -4.705 20.946 120.330
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 168.85616 12.31080 13.716 < 2e-16 ***
## s_1 -2.87654 0.70160 -4.100 4.17e-05 ***
## atr -0.19359 0.03289 -5.886 4.11e-09 ***
## k_1 -1.44046 0.23506 -6.128 9.32e-10 ***
## al_1 -1.61502 0.49033 -3.294 0.000993 ***
## mo_1 -0.25834 0.11202 -2.306 0.021131 *
## mg_1 0.78110 0.17500 4.463 8.18e-06 ***
## ph_cacl2_1 -3.46843 1.01665 -3.412 0.000649 ***
## ctc_1 -8.87523 2.85928 -3.104 0.001916 **
## p_resina_1 1.45841 0.69956 2.085 0.037125 *
## m_1 -1.18414 0.79451 -1.490 0.136160
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.39 on 7950 degrees of freedom
## Multiple R-squared: 0.02705, Adjusted R-squared: 0.02582
## F-statistic: 22.1 on 10 and 7950 DF, p-value: < 2.2e-16
## [1] "10. PCA e biplot"
## [1] 5.757158138 2.041460729 1.206098965 1.019566277 0.937435399 0.912317882
## [7] 0.852424064 0.737417569 0.637598621 0.372596423 0.292616262 0.202191377
## [13] 0.019741922 0.008438288 0.002938084
## [1] 0.3838105425 0.1360973819 0.0804065976 0.0679710852 0.0624956933
## [6] 0.0608211921 0.0568282709 0.0491611713 0.0425065747 0.0248397615
## [11] 0.0195077508 0.0134794251 0.0013161282 0.0005625525 0.0001958722
## [1] 38.38105 51.99079 60.03145 66.82856 73.07813 79.16025 84.84308
## [8] 89.75919 94.00985 96.49383 98.44460 99.79254 99.92416 99.98041
## [15] 100.00000
## [1] "11. Semivariograma e krigagem"
## model psill range
## 1 Nug 107.34426 0.0000000
## 2 Gau 66.61976 -0.6210678
## [using ordinary kriging]
## 0% done 5% done 9% done 13% done 17% done 21% done 24% done 28% done 31% done 35% done 38% done 42% done 45% done 49% done 52% done 55% done 59% done 63% done 66% done 70% done 74% done 79% done 83% done 88% done 92% done 97% done100% done
