homework0408
公衛所吳東翰
資料匯入
dta<-read.csv("C:/Users/User/Desktop/LearnR/CA/CAdata/lowbwt.csv")
View(dta)
attach(dta)(a) Please calculate Pearson’s correlation coefficient and p-value between LWT and BWT.
cor.test(LWT, BWT, method="pearson")##
## Pearson's product-moment correlation
##
## data: LWT and BWT
## t = 2.5856, df = 187, p-value = 0.01048
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.04423134 0.32003247
## sample estimates:
## cor
## 0.1857887(b) Then draw thescatterplotof these two variables.
plot(LWT, BWT)
with(dta, smoothScatter(LWT, BWT))
(c) Please use multiple linear regression to analyze the risk factors of BWT by all independent variables.
(Outcome: BWT; Predictors: AGE, LWT, RACE, SMOKE, PTL, HT, UI, and FTV)
(BWT, AGE, LWT, PTL, and FTV are treated as continuousvariables)
(RACE, SMOKE, HT, and UI are treated as categoricalvariables)
Hint: R code: factor(RACE)
fit= lm(BWT~AGE+LWT+factor(RACE)+factor(SMOKE)+PTL+factor(HT)+factor(UI)+FTV) #用factor 宣告x3轉成類別變項
summary(fit)##
## Call:
## lm(formula = BWT ~ AGE + LWT + factor(RACE) + factor(SMOKE) +
## PTL + factor(HT) + factor(UI) + FTV)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1826.20 -434.94 57.59 472.67 1702.68
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2930.102 312.839 9.366 < 2e-16 ***
## AGE -3.650 9.618 -0.379 0.704787
## LWT 4.354 1.735 2.509 0.012990 *
## factor(RACE)2 -489.442 149.953 -3.264 0.001316 **
## factor(RACE)3 -357.051 114.729 -3.112 0.002163 **
## factor(SMOKE)1 -350.618 106.454 -3.294 0.001192 **
## PTL -48.839 101.950 -0.479 0.632492
## factor(HT)1 -592.812 202.279 -2.931 0.003824 **
## factor(UI)1 -514.928 138.857 -3.708 0.000278 ***
## FTV -14.072 46.458 -0.303 0.762323
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 650.2 on 179 degrees of freedom
## Multiple R-squared: 0.2427, Adjusted R-squared: 0.2046
## F-statistic: 6.373 on 9 and 179 DF, p-value: 7.961e-08(d) Please use multiple linear regression to analyze the risk factors of BWT by stepwise method.
library(MASS)
step <-stepAIC(fit, direction="both") # direction = c("both", "backward", "forward") # -的 back +的for ## Start: AIC=2458.13
## BWT ~ AGE + LWT + factor(RACE) + factor(SMOKE) + PTL + factor(HT) +
## factor(UI) + FTV
##
## Df Sum of Sq RSS AIC
## - FTV 1 38784 75709672 2456.2
## - AGE 1 60875 75731762 2456.3
## - PTL 1 97013 75767900 2456.4
## <none> 75670887 2458.1
## - LWT 1 2661527 78332414 2462.7
## - factor(HT) 1 3630845 79301732 2465.0
## - factor(SMOKE) 1 4585833 80256720 2467.2
## - factor(RACE) 2 6627291 82298178 2470.0
## - factor(UI) 1 5813481 81484368 2470.1
##
## Step: AIC=2456.23
## BWT ~ AGE + LWT + factor(RACE) + factor(SMOKE) + PTL + factor(HT) +
## factor(UI)
##
## Df Sum of Sq RSS AIC
## - AGE 1 82254 75791926 2454.4
## - PTL 1 93251 75802922 2454.5
## <none> 75709672 2456.2
## + FTV 1 38784 75670887 2458.1
## - LWT 1 2623848 78333519 2460.7
## - factor(HT) 1 3592170 79301842 2463.0
## - factor(SMOKE) 1 4569078 80278749 2465.3
## - factor(RACE) 2 6601034 82310705 2468.0
## - factor(UI) 1 5791945 81501616 2468.2
##
## Step: AIC=2454.43
## BWT ~ LWT + factor(RACE) + factor(SMOKE) + PTL + factor(HT) +
## factor(UI)
##
## Df Sum of Sq RSS AIC
## - PTL 1 119803 75911729 2452.7
## <none> 75791926 2454.4
## + AGE 1 82254 75709672 2456.2
## + FTV 1 60164 75731762 2456.3
## - LWT 1 2542283 78334209 2458.7
## - factor(HT) 1 3545242 79337168 2461.1
## - factor(SMOKE) 1 4490240 80282166 2463.3
## - factor(UI) 1 5723278 81515204 2466.2
## - factor(RACE) 2 6614759 82406685 2466.2
##
## Step: AIC=2452.73
## BWT ~ LWT + factor(RACE) + factor(SMOKE) + factor(HT) + factor(UI)
##
## Df Sum of Sq RSS AIC
## <none> 75911729 2452.7
## + PTL 1 119803 75791926 2454.4
## + AGE 1 108807 75802922 2454.5
## + FTV 1 58868 75852861 2454.6
## - LWT 1 2671613 78583342 2457.3
## - factor(HT) 1 3583850 79495579 2459.4
## - factor(SMOKE) 1 4911219 80822948 2462.6
## - factor(RACE) 2 6674129 82585858 2464.7
## - factor(UI) 1 6327025 82238754 2465.9step$anova # display results## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## BWT ~ AGE + LWT + factor(RACE) + factor(SMOKE) + PTL + factor(HT) +
## factor(UI) + FTV
##
## Final Model:
## BWT ~ LWT + factor(RACE) + factor(SMOKE) + factor(HT) + factor(UI)
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 179 75670887 2458.130
## 2 - FTV 1 38784.31 180 75709672 2456.227
## 3 - AGE 1 82254.45 181 75791926 2454.432
## 4 - PTL 1 119802.88 182 75911729 2452.730