Basic Data Analysis Workshop - Hanoi
Thach Tran
2024-08-20
Chương trình tập huấn phân tích dữ liệu bằng ngôn ngữ R - BV 108
Ngày 4: Hồi qui tuyến tính
Việc 1. Đọc dữ liệu vào R
ob = read.csv("C:\\Thach\\VN trips\\2024_2Aug\\Data Analysis workshop (Hospital 108)\\Datasets\\obesity data.csv")Việc 2. Đánh giá mối liên quan giữa tuổi và mật độ xương toàn thân
2.1 Biểu đồ histogram đánh giá phân bố của tuổi và mật độ xương toàn thân
library(ggplot2)
library(gridExtra)
p = ggplot(data = ob, aes(x = age))
p1 = p + geom_histogram(fill = "blue", col = "white") + labs(x = "Tuổi (năm)", y = "Số người", title = "Phân bố tuổi")
p = ggplot(data = ob, aes(x = wbbmd))
p2 = p + geom_histogram(fill = "blue", col = "white") + labs(x = "Mật độ xương toàn thân (g/cm2)", y = "Số người", title = "Phân bố MĐX toàn thân")
grid.arrange(p1, p2, ncol = 2)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
2.2 Biểu đồ tán xạ đánh giá mối liên quan giữa tuổi và MĐX toàn thân
p = ggplot(data = ob, aes(x = age, y = wbbmd))
p + geom_point() + geom_smooth(method = "lm", formula = y~ x)
2.3 Phân tích tương quan đánh giá mối liên quan giữa tuổi và MĐX toàn thân
cor.test(ob$age, ob$wbbmd, method= "pearson")##
## Pearson's product-moment correlation
##
## data: ob$age and ob$wbbmd
## t = -17.154, df = 1215, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4856972 -0.3951677
## sample estimates:
## cor
## -0.4415556Việc 3. Mô hình tuyến tính đánh giá mối liên quan giữa tuổi và MĐX toàn thân
3.1 Thực hiện mô hình hồi qui
m.1 = lm(wbbmd ~ age, data = ob)
summary(m.1)##
## Call:
## lm(formula = wbbmd ~ age, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.32749 -0.07268 -0.00533 0.06793 0.33178
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.1450766 0.0084638 135.29 <2e-16 ***
## age -0.0028914 0.0001686 -17.15 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1015 on 1215 degrees of freedom
## Multiple R-squared: 0.195, Adjusted R-squared: 0.1943
## F-statistic: 294.3 on 1 and 1215 DF, p-value: < 2.2e-163.2 Đánh giá giả định của mô hình
par(mfrow = c(2,2))
plot(m.1)
library(ggfortify)## Warning: package 'ggfortify' was built under R version 4.3.2autoplot(m.1)
3.3 Trình bày kết quả
Việc 4. Đánh giá mối liên quan giữa tuổi và giới tính với MĐX toàn thân
4.1 Biểu đồ tán xạ đánh giá mối liên quan giữa tuổi với MĐX toàn thân theo giới tính
p = ggplot(data = ob, aes(x = age, y = wbbmd, fill = gender, col = gender))
p1 = p + geom_point() + geom_smooth() + labs(x = "Tuổi (năm)", y = "Mật độ xương toàn thân (g/cm2)") + ggtitle("Liên quan giữa tuổi và MĐX theo giới tính")
p1## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
4.2 Nhận xét về ảnh hưởng của giới tính lên mối liên quan giữa tuổi với MĐX toàn thân
4.3 Thực hiện mô hình hồi qui tuyến tính
m.2 = lm(wbbmd ~ age + gender, data = ob)
summary(m.2)##
## Call:
## lm(formula = wbbmd ~ age + gender, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.36272 -0.06658 -0.00411 0.06549 0.34473
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.118288 0.008636 129.485 <2e-16 ***
## age -0.002691 0.000164 -16.408 <2e-16 ***
## genderM 0.059417 0.006230 9.537 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09798 on 1214 degrees of freedom
## Multiple R-squared: 0.2511, Adjusted R-squared: 0.2498
## F-statistic: 203.5 on 2 and 1214 DF, p-value: < 2.2e-164.4 Kiểm tra giả định mô hình
par(mfrow = c(2,2))
plot(m.2)
autoplot(m.2)
4.5 Đánh giá kết quả
summary(m.2)##
## Call:
## lm(formula = wbbmd ~ age + gender, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.36272 -0.06658 -0.00411 0.06549 0.34473
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.118288 0.008636 129.485 <2e-16 ***
## age -0.002691 0.000164 -16.408 <2e-16 ***
## genderM 0.059417 0.006230 9.537 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09798 on 1214 degrees of freedom
## Multiple R-squared: 0.2511, Adjusted R-squared: 0.2498
## F-statistic: 203.5 on 2 and 1214 DF, p-value: < 2.2e-16Việc 5. Xây dựng mô hình dự báo MĐX
5.1 Đọc dữ liệu ‘Oxteo-data.xlsx’ và gọi đối tượng là ‘fx’
library(readxl)
fx = as.data.frame(read_excel("C:\\Thach\\VN trips\\2024_2Aug\\Data Analysis workshop (Hospital 108)\\Datasets\\Osteo-data.xlsx"))
dim(fx)## [1] 2216 17summary(fx)## id sex age weight
## Min. : 1.0 Length:2216 Min. :57.00 Min. : 34.00
## 1st Qu.: 554.8 Class :character 1st Qu.:65.00 1st Qu.: 60.00
## Median :1108.5 Mode :character Median :70.00 Median : 69.00
## Mean :1108.5 Mean :70.89 Mean : 70.14
## 3rd Qu.:1662.2 3rd Qu.:76.00 3rd Qu.: 79.00
## Max. :2216.0 Max. :96.00 Max. :133.00
## NA's :53
## height prior_fx fnbmd smoking
## Min. :136.0 Min. :0.0000 Min. :0.2800 Min. :0.0000
## 1st Qu.:158.0 1st Qu.:0.0000 1st Qu.:0.7300 1st Qu.:0.0000
## Median :164.0 Median :0.0000 Median :0.8200 Median :0.0000
## Mean :164.9 Mean :0.1476 Mean :0.8287 Mean :0.4176
## 3rd Qu.:171.0 3rd Qu.:0.0000 3rd Qu.:0.9300 3rd Qu.:1.0000
## Max. :196.0 Max. :1.0000 Max. :1.5100 Max. :1.0000
## NA's :54 NA's :89 NA's :1
## parkinson rheum hypertension diabetes
## Min. :0.00000 Min. :0.00000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.000
## Median :0.00000 Median :0.00000 Median :1.0000 Median :0.000
## Mean :0.06498 Mean :0.03881 Mean :0.5063 Mean :0.111
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:0.000
## Max. :1.00000 Max. :1.00000 Max. :1.0000 Max. :1.000
##
## copd cancer cvd falls_n
## Min. :0.000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.111 Mean :0.08529 Mean :0.3872 Mean :0.2843
## 3rd Qu.:0.000 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.000 Max. :1.00000 Max. :1.0000 Max. :2.0000
##
## fx
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.2595
## 3rd Qu.:1.0000
## Max. :1.0000
## 5.2 Mô tả đặc điểm của dữ liệu theo giớ tính
library(table1)##
## Attaching package: 'table1'## The following objects are masked from 'package:base':
##
## units, units<-table1(~ age + weight + height + fnbmd + as.factor(prior_fx) + as.factor(falls_n) + as.factor(smoking) + as.factor(parkinson) + as.factor(rheum) + as.factor(hypertension) + as.factor(diabetes) + as.factor(copd) + as.factor(cancer) + as.factor(cvd) + as.factor(fx) | sex, data = fx)| Female (N=1358) |
Male (N=858) |
Overall (N=2216) |
|
|---|---|---|---|
| age | |||
| Mean (SD) | 71.2 (7.59) | 70.4 (6.44) | 70.9 (7.17) |
| Median [Min, Max] | 70.0 [57.0, 96.0] | 69.0 [59.0, 92.0] | 70.0 [57.0, 96.0] |
| weight | |||
| Mean (SD) | 64.9 (12.5) | 78.2 (12.7) | 70.1 (14.2) |
| Median [Min, Max] | 64.0 [34.0, 115] | 78.0 [45.0, 133] | 69.0 [34.0, 133] |
| Missing | 42 (3.1%) | 11 (1.3%) | 53 (2.4%) |
| height | |||
| Mean (SD) | 160 (6.37) | 173 (6.86) | 165 (9.35) |
| Median [Min, Max] | 160 [136, 181] | 173 [151, 196] | 164 [136, 196] |
| Missing | 41 (3.0%) | 13 (1.5%) | 54 (2.4%) |
| fnbmd | |||
| Mean (SD) | 0.777 (0.132) | 0.909 (0.153) | 0.829 (0.155) |
| Median [Min, Max] | 0.770 [0.280, 1.31] | 0.900 [0.340, 1.51] | 0.820 [0.280, 1.51] |
| Missing | 57 (4.2%) | 32 (3.7%) | 89 (4.0%) |
| as.factor(prior_fx) | |||
| 0 | 1146 (84.4%) | 743 (86.6%) | 1889 (85.2%) |
| 1 | 212 (15.6%) | 115 (13.4%) | 327 (14.8%) |
| as.factor(falls_n) | |||
| 0 | 1063 (78.3%) | 671 (78.2%) | 1734 (78.2%) |
| 1 | 206 (15.2%) | 128 (14.9%) | 334 (15.1%) |
| 2 | 89 (6.6%) | 59 (6.9%) | 148 (6.7%) |
| as.factor(smoking) | |||
| 0 | 962 (70.8%) | 328 (38.2%) | 1290 (58.2%) |
| 1 | 395 (29.1%) | 530 (61.8%) | 925 (41.7%) |
| Missing | 1 (0.1%) | 0 (0%) | 1 (0.0%) |
| as.factor(parkinson) | |||
| 0 | 1268 (93.4%) | 804 (93.7%) | 2072 (93.5%) |
| 1 | 90 (6.6%) | 54 (6.3%) | 144 (6.5%) |
| as.factor(rheum) | |||
| 0 | 1306 (96.2%) | 824 (96.0%) | 2130 (96.1%) |
| 1 | 52 (3.8%) | 34 (4.0%) | 86 (3.9%) |
| as.factor(hypertension) | |||
| 0 | 695 (51.2%) | 399 (46.5%) | 1094 (49.4%) |
| 1 | 663 (48.8%) | 459 (53.5%) | 1122 (50.6%) |
| as.factor(diabetes) | |||
| 0 | 1213 (89.3%) | 757 (88.2%) | 1970 (88.9%) |
| 1 | 145 (10.7%) | 101 (11.8%) | 246 (11.1%) |
| as.factor(copd) | |||
| 0 | 1211 (89.2%) | 759 (88.5%) | 1970 (88.9%) |
| 1 | 147 (10.8%) | 99 (11.5%) | 246 (11.1%) |
| as.factor(cancer) | |||
| 0 | 1235 (90.9%) | 792 (92.3%) | 2027 (91.5%) |
| 1 | 123 (9.1%) | 66 (7.7%) | 189 (8.5%) |
| as.factor(cvd) | |||
| 0 | 843 (62.1%) | 515 (60.0%) | 1358 (61.3%) |
| 1 | 515 (37.9%) | 343 (40.0%) | 858 (38.7%) |
| as.factor(fx) | |||
| 0 | 932 (68.6%) | 709 (82.6%) | 1641 (74.1%) |
| 1 | 426 (31.4%) | 149 (17.4%) | 575 (25.9%) |
5.3 Xây dựng mô hình dự báo MD0X tại cổ xương đùi
Phương pháp stepwise
fx.2 = na.omit(fx)
m.step = lm(fnbmd ~ age + sex + weight + height + fnbmd + prior_fx + falls_n + smoking + parkinson + rheum + hypertension + diabetes + copd + cancer + cvd, data = fx.2)
step = step(m.step)## Start: AIC=-9093.64
## fnbmd ~ age + sex + weight + height + fnbmd + prior_fx + falls_n +
## smoking + parkinson + rheum + hypertension + diabetes + copd +
## cancer + cvd
##
##
## Step: AIC=-9093.64
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## parkinson + rheum + hypertension + diabetes + copd + cancer +
## cvd
##
## Df Sum of Sq RSS AIC
## - copd 1 0.0002 28.734 -9095.6
## - cvd 1 0.0024 28.736 -9095.5
## - hypertension 1 0.0034 28.737 -9095.4
## - parkinson 1 0.0071 28.741 -9095.1
## - cancer 1 0.0075 28.741 -9095.1
## - diabetes 1 0.0082 28.742 -9095.0
## - falls_n 1 0.0134 28.747 -9094.7
## <none> 28.734 -9093.6
## - rheum 1 0.0446 28.778 -9092.3
## - height 1 0.1631 28.897 -9083.6
## - prior_fx 1 0.2419 28.976 -9077.9
## - smoking 1 0.3836 29.117 -9067.5
## - sex 1 0.8175 29.551 -9036.1
## - age 1 2.1555 30.889 -8942.2
## - weight 1 5.0206 33.754 -8754.1
##
## Step: AIC=-9095.62
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## parkinson + rheum + hypertension + diabetes + cancer + cvd
##
## Df Sum of Sq RSS AIC
## - cvd 1 0.0025 28.736 -9097.4
## - hypertension 1 0.0034 28.737 -9097.4
## - parkinson 1 0.0071 28.741 -9097.1
## - cancer 1 0.0075 28.741 -9097.1
## - diabetes 1 0.0082 28.742 -9097.0
## - falls_n 1 0.0133 28.747 -9096.6
## <none> 28.734 -9095.6
## - rheum 1 0.0447 28.779 -9094.3
## - height 1 0.1630 28.897 -9085.6
## - prior_fx 1 0.2418 28.976 -9079.9
## - smoking 1 0.3834 29.117 -9069.5
## - sex 1 0.8180 29.552 -9038.1
## - age 1 2.1586 30.892 -8944.0
## - weight 1 5.0207 33.755 -8756.1
##
## Step: AIC=-9097.44
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## parkinson + rheum + hypertension + diabetes + cancer
##
## Df Sum of Sq RSS AIC
## - hypertension 1 0.0041 28.740 -9099.1
## - parkinson 1 0.0071 28.743 -9098.9
## - diabetes 1 0.0074 28.744 -9098.9
## - cancer 1 0.0077 28.744 -9098.9
## - falls_n 1 0.0133 28.750 -9098.5
## <none> 28.736 -9097.4
## - rheum 1 0.0440 28.780 -9096.2
## - height 1 0.1628 28.899 -9087.5
## - prior_fx 1 0.2418 28.978 -9081.7
## - smoking 1 0.3849 29.121 -9071.2
## - sex 1 0.8181 29.554 -9039.9
## - age 1 2.1581 30.894 -8945.9
## - weight 1 5.0198 33.756 -8758.0
##
## Step: AIC=-9099.14
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## parkinson + rheum + diabetes + cancer
##
## Df Sum of Sq RSS AIC
## - diabetes 1 0.0064 28.747 -9100.7
## - parkinson 1 0.0074 28.748 -9100.6
## - cancer 1 0.0077 28.748 -9100.6
## - falls_n 1 0.0130 28.753 -9100.2
## <none> 28.740 -9099.1
## - rheum 1 0.0442 28.785 -9097.9
## - height 1 0.1636 28.904 -9089.1
## - prior_fx 1 0.2409 28.981 -9083.4
## - smoking 1 0.3830 29.123 -9073.1
## - sex 1 0.8148 29.555 -9041.8
## - age 1 2.1568 30.897 -8947.7
## - weight 1 5.0175 33.758 -8759.8
##
## Step: AIC=-9100.66
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## parkinson + rheum + cancer
##
## Df Sum of Sq RSS AIC
## - parkinson 1 0.0078 28.755 -9102.1
## - cancer 1 0.0080 28.755 -9102.1
## - falls_n 1 0.0129 28.760 -9101.7
## <none> 28.747 -9100.7
## - rheum 1 0.0449 28.792 -9099.3
## - height 1 0.1622 28.909 -9090.7
## - prior_fx 1 0.2425 28.989 -9084.8
## - smoking 1 0.3820 29.129 -9074.7
## - sex 1 0.8189 29.566 -9043.1
## - age 1 2.1640 30.911 -8948.7
## - weight 1 5.0200 33.767 -8761.3
##
## Step: AIC=-9102.09
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## rheum + cancer
##
## Df Sum of Sq RSS AIC
## - cancer 1 0.0080 28.763 -9103.5
## - falls_n 1 0.0127 28.767 -9103.2
## <none> 28.755 -9102.1
## - rheum 1 0.0454 28.800 -9100.7
## - height 1 0.1622 28.917 -9092.2
## - prior_fx 1 0.2407 28.995 -9086.4
## - smoking 1 0.3823 29.137 -9076.1
## - sex 1 0.8188 29.573 -9044.5
## - age 1 2.1706 30.925 -8949.7
## - weight 1 5.0248 33.779 -8762.5
##
## Step: AIC=-9103.5
## fnbmd ~ age + sex + weight + height + prior_fx + falls_n + smoking +
## rheum
##
## Df Sum of Sq RSS AIC
## - falls_n 1 0.0132 28.776 -9104.5
## <none> 28.763 -9103.5
## - rheum 1 0.0471 28.810 -9102.0
## - height 1 0.1640 28.927 -9093.4
## - prior_fx 1 0.2405 29.003 -9087.8
## - smoking 1 0.3877 29.150 -9077.1
## - sex 1 0.8209 29.584 -9045.8
## - age 1 2.1644 30.927 -8951.6
## - weight 1 5.0254 33.788 -8764.0
##
## Step: AIC=-9104.53
## fnbmd ~ age + sex + weight + height + prior_fx + smoking + rheum
##
## Df Sum of Sq RSS AIC
## <none> 28.776 -9104.5
## - rheum 1 0.0484 28.824 -9103.0
## - height 1 0.1665 28.942 -9094.3
## - prior_fx 1 0.2443 29.020 -9088.6
## - smoking 1 0.3930 29.169 -9077.8
## - sex 1 0.8192 29.595 -9047.0
## - age 1 2.1621 30.938 -8952.9
## - weight 1 5.0190 33.795 -8765.5summary(step)##
## Call:
## lm(formula = fnbmd ~ age + sex + weight + height + prior_fx +
## smoking + rheum, data = fx.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37449 -0.07631 -0.00732 0.06924 0.56471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6089875 0.0759281 8.021 1.73e-15 ***
## age -0.0048301 0.0003833 -12.600 < 2e-16 ***
## sexMale 0.0602003 0.0077620 7.756 1.35e-14 ***
## weight 0.0043244 0.0002253 19.198 < 2e-16 ***
## height 0.0015153 0.0004334 3.496 0.000481 ***
## prior_fx -0.0311566 0.0073569 -4.235 2.38e-05 ***
## smoking -0.0290938 0.0054157 -5.372 8.64e-08 ***
## rheum 0.0246442 0.0130749 1.885 0.059587 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1167 on 2113 degrees of freedom
## Multiple R-squared: 0.4332, Adjusted R-squared: 0.4313
## F-statistic: 230.7 on 7 and 2113 DF, p-value: < 2.2e-165.3.2 Phương pháp BMA
library(BMA)## Loading required package: survival## Loading required package: leaps## Loading required package: robustbase##
## Attaching package: 'robustbase'## The following object is masked from 'package:survival':
##
## heart## Loading required package: inline## Loading required package: rrcov## Scalable Robust Estimators with High Breakdown Point (version 1.7-4)xvars = fx.2[, c("age", "sex", "weight", "height", "prior_fx", "falls_n", "smoking", "parkinson", "rheum", "hypertension", "diabetes", "copd", "cancer", "cvd")]
m.bma = bicreg(xvars, fx.2$fnbmd, strict = FALSE, OR = 20)
summary(m.bma)##
## Call:
## bicreg(x = xvars, y = fx.2$fnbmd, strict = FALSE, OR = 20)
##
##
## 3 models were selected
## Best 3 models (cumulative posterior probability = 1 ):
##
## p!=0 EV SD model 1 model 2 model 3
## Intercept 100.0 0.624291 0.0969317 6.062e-01 6.090e-01 8.477e-01
## age 100.0 -0.004836 0.0003879 -4.817e-03 -4.830e-03 -5.050e-03
## sexMale 100.0 0.061274 0.0088264 6.002e-02 6.020e-02 7.683e-02
## weight 100.0 0.004350 0.0002376 4.329e-03 4.324e-03 4.629e-03
## height 92.6 0.001417 0.0005777 1.531e-03 1.515e-03 .
## prior_fx 100.0 -0.031084 0.0073646 -3.101e-02 -3.116e-02 -3.180e-02
## falls_n 0.0 0.000000 0.0000000 . . .
## smoking 100.0 -0.029203 0.0054195 -2.921e-02 -2.909e-02 -2.929e-02
## parkinson 0.0 0.000000 0.0000000 . . .
## rheum 10.7 0.002638 0.0087381 . 2.464e-02 .
## hypertension 0.0 0.000000 0.0000000 . . .
## diabetes 0.0 0.000000 0.0000000 . . .
## copd 0.0 0.000000 0.0000000 . . .
## cancer 0.0 0.000000 0.0000000 . . .
## cvd 0.0 0.000000 0.0000000 . . .
##
## nVar 6 7 5
## r2 0.432 0.433 0.429
## BIC -1.155e+03 -1.151e+03 -1.150e+03
## post prob 0.819 0.107 0.074imageplot.bma(m.bma)
5.4 Kiểm tra giả định của mô hình
m.bmd = lm(fnbmd ~ age + sex + weight + height + prior_fx + smoking, data = fx.2)
summary(m.bmd)##
## Call:
## lm(formula = fnbmd ~ age + sex + weight + height + prior_fx +
## smoking, data = fx.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37332 -0.07653 -0.00745 0.07113 0.58841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6062028 0.0759596 7.981 2.37e-15 ***
## age -0.0048171 0.0003835 -12.561 < 2e-16 ***
## sexMale 0.0600151 0.0077660 7.728 1.68e-14 ***
## weight 0.0043288 0.0002254 19.206 < 2e-16 ***
## height 0.0015312 0.0004335 3.532 0.000422 ***
## prior_fx -0.0310094 0.0073609 -4.213 2.63e-05 ***
## smoking -0.0292099 0.0054186 -5.391 7.80e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1168 on 2114 degrees of freedom
## Multiple R-squared: 0.4322, Adjusted R-squared: 0.4306
## F-statistic: 268.2 on 6 and 2114 DF, p-value: < 2.2e-16par(mfrow = c(2,2))
plot(m.bmd)
5.5 Viết công thức của mô hình tối ưu
summary(m.bmd)##
## Call:
## lm(formula = fnbmd ~ age + sex + weight + height + prior_fx +
## smoking, data = fx.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37332 -0.07653 -0.00745 0.07113 0.58841
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.6062028 0.0759596 7.981 2.37e-15 ***
## age -0.0048171 0.0003835 -12.561 < 2e-16 ***
## sexMale 0.0600151 0.0077660 7.728 1.68e-14 ***
## weight 0.0043288 0.0002254 19.206 < 2e-16 ***
## height 0.0015312 0.0004335 3.532 0.000422 ***
## prior_fx -0.0310094 0.0073609 -4.213 2.63e-05 ***
## smoking -0.0292099 0.0054186 -5.391 7.80e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1168 on 2114 degrees of freedom
## Multiple R-squared: 0.4322, Adjusted R-squared: 0.4306
## F-statistic: 268.2 on 6 and 2114 DF, p-value: < 2.2e-16