The IQ scores and behavioral problem scores of children at age 5 were examined depending on whether or not their mothers had suffered an episode of post-natal depression.

讀入資料

dta <- read.table("D:/201802/data_management/w3/IQ_Beh.txt", header = T, row.names = 1)
str(dta)
'data.frame':   94 obs. of  3 variables:
 $ Dep: Factor w/ 2 levels "D","N": 2 2 2 2 1 2 2 2 2 2 ...
 $ IQ : int  103 124 124 104 96 92 124 99 92 116 ...
 $ BP : int  4 12 9 3 3 3 6 4 3 9 ...
head(dta)
  Dep  IQ BP
1   N 103  4
2   N 124 12
3   N 124  9
4   N 104  3
5   D  96  3
6   N  92  3
class(dta)
[1] "data.frame"
dim(dta)
[1] 94  3
names(dta)
[1] "Dep" "IQ"  "BP" 
is.vector(dta$BP)
[1] TRUE
dta[1, ]
  Dep  IQ BP
1   N 103  4
dta[1:3, "IQ"]
[1] 103 124 124
tail(dta[order(dta$BP), ])
   Dep  IQ BP
16   N  89 11
58   N 117 11
66   N 126 11
2    N 124 12
73   D  99 13
12   D  22 17
tail(dta[order(-dta$BP), ], 4)
   Dep  IQ BP
77   N 124  1
80   N 121  1
24   N 106  0
75   N 122  0

作圖

# histogram of IQ
with(dta, hist(IQ, xlab = "IQ", main = ""))

# boxplot of behavior problem by depression status
boxplot(BP ~ Dep, data = dta, 
        xlab = "Depression", 
        ylab = "Behavior problem score")

# scatter plot
plot(IQ ~ BP, data = dta, pch = 20, col = dta$Dep, 
     xlab = "Behavior problem score", ylab = "IQ")
grid()

# two regression lines
plot(BP ~ IQ, data = dta, type = "n",
     ylab = "Behavior problem score", xlab = "IQ")
text(dta$IQ, dta$BP, labels = dta$Dep, cex = 0.5)
abline(lm(BP ~ IQ, data = dta, subset = Dep == "D"))
abline(lm(BP ~ IQ, data = dta, subset = Dep == "N"), lty = 2)

  1. Did the two groups of children have different IQ and/or behavioral problems? Yes
summary(manova(cbind(BP, IQ) ~ Dep, data = dta))
          Df   Pillai approx F num Df den Df  Pr(>F)  
Dep        1 0.072039   3.5322      2     91 0.03331 *
Residuals 92                                          
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  1. Was there any evidence of a relationship between IQ and behavioral problems?
    兩者為負向關係，BP每增加一單位，IQ下降2
summary(lm(IQ ~ BP, data = dta))

Call:
lm(formula = IQ ~ BP, data = dta)

Residuals:
    Min      1Q  Median      3Q     Max 
-66.153  -9.223   0.773   8.788  28.789 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 122.2425     3.4115  35.832  < 2e-16 ***
BP           -2.0053     0.5265  -3.809 0.000252 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 16.21 on 92 degrees of freedom
Multiple R-squared:  0.1362,    Adjusted R-squared:  0.1268 
F-statistic: 14.51 on 1 and 92 DF,  p-value: 0.0002518