Phân tích dữ liệu bằng ngôn ngữ R - BV SIS Cần Thơ
Thach Tran
2024-12-28
Chương trình tập huấn phân tích dữ liệu bằng ngôn ngữ R - BV SIS Cần Thơ (2-6/1/2025)
Ngày 3: Hồi qui tuyến tính
Phân tích tương quan
Việc 1. Đọc dữ liệu vào R
df = read.csv("C:\\Thach\\VN trips\\2024_4Dec\\SIS Can Tho\\Datasets\\Bone data.csv")Việc 2. Đánh giá mối liên quan giữa cân nặng và mật độ xương cổ xương đùi
2.1 Vẽ biểu đồ đánh giá mối liên quan giữa cân nặng và mật độ xương cổ xương đùi
library(ggplot2)
p = ggplot(data = df, aes(x = weight, y = fnbmd))
p + geom_point() + geom_smooth()## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'## Warning: Removed 41 rows containing non-finite values (`stat_smooth()`).## Warning: Removed 41 rows containing missing values (`geom_point()`).
2.2 Phân tích đánh giá tương quan giữa cân nặng và mật độ cổ xương đùi
library(lessR)## Warning: package 'lessR' was built under R version 4.3.3##
## lessR 4.3.9 feedback: gerbing@pdx.edu
## --------------------------------------------------------------
## > d <- Read("") Read text, Excel, SPSS, SAS, or R data file
## d is default data frame, data= in analysis routines optional
##
## Many examples of reading, writing, and manipulating data,
## graphics, testing means and proportions, regression, factor analysis,
## customization, and descriptive statistics from pivot tables
## Enter: browseVignettes("lessR")
##
## View lessR updates, now including time series forecasting
## Enter: news(package="lessR")
##
## Interactive data analysis
## Enter: interact()Correlation(weight, fnbmd, data = df)## Correlation Analysis for Variables weight and fnbmd
##
##
## >>> Pearson's product-moment correlation
##
## Number of paired values with neither missing, n = 2121
## Number of cases (rows of data) deleted: 41
##
## Sample Covariance: s = 1.269
##
## Sample Correlation: r = 0.581
##
## Hypothesis Test of 0 Correlation: t = 32.882, df = 2119, p-value = 0.000
## 95% Confidence Interval for Correlation: 0.552 to 0.609Việc 3. Đánh giá mối tương quan đa biến
vars = df[, c("sex", "age", "weight", "height", "fnbmd")]
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2ggpairs(data = vars, mapping = aes(color = sex))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Việc 4. Đọc dữ liệu vào R
ob = read.csv("C:\\Thach\\VN trips\\2024_4Dec\\SIS Can Tho\\Datasets\\Obesity data.csv")Việc 5. So sánh tỉ trọng mỡ giữa nam và nữ
5.1 Vẽ biểu đồ hộp so sánh tỉ trọng mỡ giữa nam và nữ
p = ggplot(data = ob, aes(x = gender, y = pcfat, col = gender))
p1 = p + geom_boxplot()
p1
5.2 Sử dụng kiểm định t
library(lessR)
ttest(pcfat ~ gender, data = ob)##
## Compare pcfat across gender with levels F and M
## Grouping Variable: gender
## Response Variable: pcfat
##
##
## ------ Describe ------
##
## pcfat for gender F: n.miss = 0, n = 862, mean = 34.672, sd = 5.187
## pcfat for gender M: n.miss = 0, n = 355, mean = 24.156, sd = 5.764
##
## Mean Difference of pcfat: 10.516
##
## Weighted Average Standard Deviation: 5.362
##
##
## ------ Assumptions ------
##
## Note: These hypothesis tests can perform poorly, and the
## t-test is typically robust to violations of assumptions.
## Use as heuristic guides instead of interpreting literally.
##
## Null hypothesis, for each group, is a normal distribution of pcfat.
## Group F: Sample mean assumed normal because n > 30, so no test needed.
## Group M: Sample mean assumed normal because n > 30, so no test needed.
##
## Null hypothesis is equal variances of pcfat, homogeneous.
## Variance Ratio test: F = 33.223/26.909 = 1.235, df = 354;861, p-value = 0.016
## Levene's test, Brown-Forsythe: t = -2.232, df = 1215, p-value = 0.026
##
##
## ------ Infer ------
##
## --- Assume equal population variances of pcfat for each gender
##
## t-cutoff for 95% range of variation: tcut = 1.962
## Standard Error of Mean Difference: SE = 0.338
##
## Hypothesis Test of 0 Mean Diff: t-value = 31.101, df = 1215, p-value = 0.000
##
## Margin of Error for 95% Confidence Level: 0.663
## 95% Confidence Interval for Mean Difference: 9.853 to 11.180
##
##
## --- Do not assume equal population variances of pcfat for each gender
##
## t-cutoff: tcut = 1.964
## Standard Error of Mean Difference: SE = 0.353
##
## Hypothesis Test of 0 Mean Diff: t = 29.768, df = 602.015, p-value = 0.000
##
## Margin of Error for 95% Confidence Level: 0.694
## 95% Confidence Interval for Mean Difference: 9.823 to 11.210
##
##
## ------ Effect Size ------
##
## --- Assume equal population variances of pcfat for each gender
##
## Standardized Mean Difference of pcfat, Cohen's d: 1.961
##
##
## ------ Practical Importance ------
##
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
##
##
## ------ Graphics Smoothing Parameter ------
##
## Density bandwidth for gender F: 1.475
## Density bandwidth for gender M: 1.867
5.3 Sử dụng mô hình hồi qui tuyến tính
m.1 = lm(pcfat ~ gender, data = ob)
summary(m.1)##
## Call:
## lm(formula = pcfat ~ gender, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.0724 -3.2724 0.1484 3.6276 14.8439
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.6724 0.1826 189.9 <0.0000000000000002 ***
## genderM -10.5163 0.3381 -31.1 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.362 on 1215 degrees of freedom
## Multiple R-squared: 0.4432, Adjusted R-squared: 0.4428
## F-statistic: 967.3 on 1 and 1215 DF, p-value: < 0.00000000000000022Dùng gói lessR
library(lessR)
m.2 = reg(pcfat ~ gender, data = ob)##
## >>> gender is not numeric. Converted to indicator variables.
m.2## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(pcfat ~ gender, data=ob, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: ob
##
## Response Variable: pcfat
## Predictor Variable: genderM
##
## Number of cases (rows) of data: 1217
## Number of cases retained for analysis: 1217
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 34.672413 0.182622 189.859 0.000 34.314123 35.030703
## genderM -10.516344 0.338131 -31.101 0.000 -11.179729 -9.852959
##
## Standard deviation of pcfat: 7.182862
##
## Standard deviation of residuals: 5.361759 for df=1215
## 95% range of residuals: 21.038669 = 2 * (1.962 * 5.361759)
##
## R-squared: 0.443 Adjusted R-squared: 0.443 PRESS R-squared: 0.441
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 967.297 df: 1 and 1215 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Model 1 27808.311497 27808.311497 967.297285 0.000
## Residuals 1215 34929.384159 28.748464
## pcfat 1216 62737.695656 51.593500
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
## pcfat genderM
## pcfat 1.00 -0.67
## genderM -0.67 1.00
##
##
## RESIDUALS AND INFLUENCE
##
## -- Data, Fitted, Residual, Studentized Residual, Dffits, Cook's Distance
## [sorted by Cook's Distance]
## [n_res_rows = 20, out of 1217 rows of data, or do n_res_rows="all"]
## ---------------------------------------------------------------------------
## genderM pcfat fitted resid rstdnt dffits cooks
## 210 1 9.200000 24.156069 -14.956069 -2.801192 -0.148882 0.011020
## 509 1 39.000000 24.156069 14.843931 2.780055 0.147758 0.010860
## 179 1 38.700000 24.156069 14.543931 2.723523 0.144754 0.010420
## 518 1 9.700000 24.156069 -14.456069 -2.706970 -0.143874 0.010300
## 200 1 9.800000 24.156069 -14.356069 -2.688132 -0.142873 0.010150
## 563 1 38.300000 24.156069 14.143931 2.648179 0.140749 0.009860
## 318 1 10.300000 24.156069 -13.856069 -2.593980 -0.137869 0.009460
## 972 1 10.300000 24.156069 -13.856069 -2.593980 -0.137869 0.009460
## 388 1 10.700000 24.156069 -13.456069 -2.518700 -0.133867 0.008920
## 203 1 11.000000 24.156069 -13.156069 -2.462262 -0.130868 0.008530
## 1137 0 14.600000 34.672413 -20.072413 -3.766065 -0.128347 0.008150
## 893 0 14.700000 34.672413 -19.972413 -3.747085 -0.127700 0.008070
## 688 1 11.400000 24.156069 -12.756069 -2.387042 -0.126870 0.008020
## 403 1 11.700000 24.156069 -12.456069 -2.330649 -0.123873 0.007640
## 858 1 11.900000 24.156069 -12.256069 -2.293064 -0.121875 0.007400
## 158 1 36.300000 24.156069 12.143931 2.271993 0.120755 0.007270
## 1106 1 36.300000 24.156069 12.143931 2.271993 0.120755 0.007270
## 827 1 36.000000 24.156069 11.843931 2.215637 0.117760 0.006910
## 756 1 12.400000 24.156069 -11.756069 -2.199135 -0.116883 0.006810
## 196 1 12.500000 24.156069 -11.656069 -2.180355 -0.115885 0.006690
##
##
## PREDICTION ERROR
##
## -- Data, Predicted, Standard Error of Prediction, 95% Prediction Intervals
## [sorted by lower bound of prediction interval]
## [to see all intervals add n_pred_rows="all"]
## ----------------------------------------------
##
## genderM pcfat pred s_pred pi.lwr pi.upr width
## 2 1 16.800000 24.156069 5.369306 13.621929 34.690209 21.068280
## 5 1 14.800000 24.156069 5.369306 13.621929 34.690209 21.068280
## ...
## 1209 1 26.400000 24.156069 5.369306 13.621929 34.690209 21.068280
## 1 0 37.300000 34.672413 5.364869 24.146979 45.197847 21.050869
## 3 0 34.000000 34.672413 5.364869 24.146979 45.197847 21.050869
## ...
## 1215 0 34.400000 34.672413 5.364869 24.146979 45.197847 21.050869
## 1216 0 41.300000 34.672413 5.364869 24.146979 45.197847 21.050869
## 1217 0 33.200000 34.672413 5.364869 24.146979 45.197847 21.050869
##
## ----------------------------------
## Plot 1: Distribution of Residuals
## Plot 2: Residuals vs Fitted Values
## ----------------------------------Kiểm tra giả định
Cách đơn giản
plot(m.1)
Dùng gói ggfortify
library(ggfortify)
autoplot(m.1)
Việc 6. Đánh giá mối liên quan giữa cân nặng và tỉ trọng mỡ
6.1 Vẽ biểu đồ tán xạ
p = ggplot(data = ob, aes(x = weight, y = pcfat))
p + geom_point() + geom_smooth()## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
6.2 Sử dụng mô hình hồi qui tuyến tính
m.3 = lm(pcfat ~ weight, data = ob)
summary(m.3)##
## Call:
## lm(formula = pcfat ~ weight, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.3122 -4.5234 0.8902 5.2695 16.9742
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 29.22295 1.22370 23.881 <0.0000000000000002 ***
## weight 0.04319 0.02188 1.975 0.0485 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.174 on 1215 degrees of freedom
## Multiple R-squared: 0.003199, Adjusted R-squared: 0.002378
## F-statistic: 3.899 on 1 and 1215 DF, p-value: 0.04855autoplot(m.3)
Việc 7. Đánh giá mối liên quan độc lập giữa cân nặng và tỉ trọng mỡ
m.4 = lm(pcfat ~ weight + age + gender + height, data = ob)
summary(m.4)##
## Call:
## lm(formula = pcfat ~ weight + age + gender + height, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.208 -2.543 0.019 2.582 15.706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 48.368722 3.505431 13.798 < 0.0000000000000002 ***
## weight 0.439169 0.015594 28.163 < 0.0000000000000002 ***
## age 0.056166 0.007404 7.585 0.0000000000000658 ***
## genderM -11.483254 0.344343 -33.348 < 0.0000000000000002 ***
## height -0.257013 0.023768 -10.813 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.974 on 1212 degrees of freedom
## Multiple R-squared: 0.695, Adjusted R-squared: 0.694
## F-statistic: 690.4 on 4 and 1212 DF, p-value: < 0.00000000000000022autoplot(m.4)
Việc 8. Xây dựng mô hình dự báo tỉ trọng mỡ
8.1 Sử dụng 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)yvar = ob[, c("pcfat")]
xvar = ob[, c("gender", "age", "height", "weight", "bmi")]
m.bma = bicreg(xvar, yvar, strict = FALSE, OR = 20)
summary(m.bma)##
## Call:
## bicreg(x = xvar, y = yvar, 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 5.26146 4.582901 7.95773 -0.79279 8.13735
## genderM 100.0 -11.25139 0.429659 -11.44430 -11.42764 -10.80625
## age 100.0 0.05259 0.008048 0.05497 0.05473 0.04715
## height 31.4 0.01759 0.028494 . 0.05598 .
## weight 39.2 0.03102 0.042611 0.07921 . .
## bmi 100.0 1.01265 0.111625 0.89419 1.08852 1.08936
##
## nVar 4 4 3
## r2 0.697 0.696 0.695
## BIC -1423.06312 -1422.62198 -1422.49027
## post prob 0.392 0.314 0.294imageplot.bma(m.bma)
8.2 Kiểm tra giả định của mô hình
m.bma = lm(pcfat ~ gender + age + weight + bmi, data = ob)
summary(m.bma)##
## Call:
## lm(formula = pcfat ~ gender + age + weight + bmi, data = ob)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.225 -2.557 0.033 2.608 15.646
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.957732 0.852500 9.335 < 0.0000000000000002 ***
## genderM -11.444303 0.342565 -33.408 < 0.0000000000000002 ***
## age 0.054966 0.007395 7.433 0.000000000000199 ***
## weight 0.079207 0.028620 2.768 0.00573 **
## bmi 0.894194 0.080297 11.136 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.963 on 1212 degrees of freedom
## Multiple R-squared: 0.6966, Adjusted R-squared: 0.6956
## F-statistic: 695.7 on 4 and 1212 DF, p-value: < 0.00000000000000022library(car)## Loading required package: carData##
## Attaching package: 'car'## The following objects are masked from 'package:lessR':
##
## bc, recode, spvif(m.bma)## gender age weight bmi
## 1.878778 1.263468 5.609651 4.663425autoplot(m.bma)
8.3 Viết phương trình
8.4 Xác định tầm quan trọng
library(relaimpo)## Loading required package: MASS## Loading required package: boot##
## Attaching package: 'boot'## The following object is masked from 'package:car':
##
## logit## The following object is masked from 'package:robustbase':
##
## salinity## The following object is masked from 'package:survival':
##
## aml## Loading required package: survey## Loading required package: grid## Loading required package: Matrix##
## Attaching package: 'survey'## The following object is masked from 'package:graphics':
##
## dotchart## Loading required package: mitools## This is the global version of package relaimpo.## If you are a non-US user, a version with the interesting additional metric pmvd is available## from Ulrike Groempings web site at prof.beuth-hochschule.de/groemping.ob$sex = ifelse(ob$gender == "F", 1, 0)
m.bma2 = lm(pcfat ~ sex + age + weight + bmi, data = ob)
calc.relimp(m.bma2, type = "lmg", rela = TRUE, rank = TRUE)## Response variable: pcfat
## Total response variance: 51.5935
## Analysis based on 1217 observations
##
## 4 Regressors:
## sex age weight bmi
## Proportion of variance explained by model: 69.66%
## Metrics are normalized to sum to 100% (rela=TRUE).
##
## Relative importance metrics:
##
## lmg
## sex 0.59317775
## age 0.06893066
## weight 0.09175463
## bmi 0.24613695
##
## Average coefficients for different model sizes:
##
## 1X 2Xs 3Xs 4Xs
## sex 10.51634414 11.71834412 11.80453842 11.44430262
## age 0.12768705 0.10445197 0.05168496 0.05496623
## weight 0.04319324 -0.05539405 -0.06907993 0.07920690
## bmi 1.03619023 1.50631405 1.54278433 0.89419395