(a) test if any pairs of the five variables: read, write, math, science, and socst, are different in means.
讀取資料、整理
library(lattice)
dta <- read.table("hs0.txt",sep='\t', head=T)
dta.1 <- stack(dta[,c(7:11)])
str(dta.1)## 'data.frame': 1000 obs. of 2 variables:
## $ values: int 57 68 44 63 47 44 50 34 63 57 ...
## $ ind : Factor w/ 5 levels "read","write",..: 1 1 1 1 1 1 1 1 1 1 ...read <- dta.1[c(1:200),]
write <- dta.1[c(201:400),]
math <- dta.1[c(401:600),]
science <- dta.1[c(601:800),]
socst <- dta.1[c(801:1000),]分組、整合
r_w <- rbind(read, write)
r_w$group <- "r_w"
r_m <- rbind(read, math)
r_m$group <- "r_m"
r_sc <- rbind(read, science)
r_sc$group <- "r_sc"
r_so <- rbind(read, socst)
r_so$group <- "r_so"
w_m <- rbind(write, math)
w_m$group <- "w_m"
w_sc <- rbind(write, science)
w_sc$group <- "w_sc"
w_so <- rbind(write, socst)
w_so$group <- "w_so"
m_sc <- rbind(math, science)
m_sc$group <- "m_sc"
m_so <- rbind(math, socst)
m_so$group <- "m_so"
sc_so <- rbind(science, socst)
sc_so$group <- "sc_so"
dat <- rbind(rbind(rbind(rbind(rbind(rbind(rbind(rbind(rbind(r_w, r_m), r_sc),
r_so), w_m), w_sc), w_so),
m_sc), m_so), sc_so)先了解各個科目的平均數、盒狀圖
## ind values
## 1 read 52.23000
## 2 write 52.77500
## 3 math 52.64500
## 4 science 51.91795
## 5 socst 52.40500
t-test
## m_sc m_so
## statistic 0.7535309 0.2382053
## parameter 391.0861 390.8348
## p.value 0.4515844 0.8118467
## conf.int Numeric,2 Numeric,2
## estimate Numeric,2 Numeric,2
## null.value 0 0
## stderr 0.9648593 1.007534
## alternative "two.sided" "two.sided"
## method "Welch Two Sample t-test" "Welch Two Sample t-test"
## data.name "x$values by x$ind" "x$values by x$ind"
## r_m r_sc
## statistic -0.4225787 0.3093215
## parameter 394.804 392.8398
## p.value 0.6728327 0.757241
## conf.int Numeric,2 Numeric,2
## estimate Numeric,2 Numeric,2
## null.value 0 0
## stderr 0.9820655 1.008825
## alternative "two.sided" "two.sided"
## method "Welch Two Sample t-test" "Welch Two Sample t-test"
## data.name "x$values by x$ind" "x$values by x$ind"
## r_so r_w
## statistic -0.166712 -0.5519906
## parameter 397.1601 395.5706
## p.value 0.8676815 0.5812665
## conf.int Numeric,2 Numeric,2
## estimate Numeric,2 Numeric,2
## null.value 0 0
## stderr 1.049714 0.9873356
## alternative "two.sided" "two.sided"
## method "Welch Two Sample t-test" "Welch Two Sample t-test"
## data.name "x$values by x$ind" "x$values by x$ind"
## sc_so w_m
## statistic -0.4712025 0.1379504
## parameter 391.2921 397.9456
## p.value 0.6377587 0.8903494
## conf.int Numeric,2 Numeric,2
## estimate Numeric,2 Numeric,2
## null.value 0 0
## stderr 1.033635 0.9423678
## alternative "two.sided" "two.sided"
## method "Welch Two Sample t-test" "Welch Two Sample t-test"
## data.name "x$values by x$ind" "x$values by x$ind"
## w_sc w_so
## statistic 0.8833551 0.3653701
## parameter 391.6689 391.9818
## p.value 0.3775863 0.7150322
## conf.int Numeric,2 Numeric,2
## estimate Numeric,2 Numeric,2
## null.value 0 0
## stderr 0.9702228 1.012672
## alternative "two.sided" "two.sided"
## method "Welch Two Sample t-test" "Welch Two Sample t-test"
## data.name "x$values by x$ind" "x$values by x$ind"Ans：No any pair of the five variables are different in means.
(b) test if the 4 different ethnic groups have the same mean scores for each of the 5 variables (individually): read, write, math, science, and socst.
先利用盒狀圖看每個族群的成績
dat$race <- dta$race
dat$ind <- as.factor(dat$ind)
bwplot(values ~ race | ind, data=dat, xlab="race", layout=c(2, 3))
切割後使用anova
## $read
## Analysis of Variance Table
##
## Response: x$values
## Df Sum Sq Mean Sq F value Pr(>F)
## factor(x$race) 3 6999 2333.08 24.22 5.262e-15 ***
## Residuals 796 76678 96.33
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $write
## Analysis of Variance Table
##
## Response: x$values
## Df Sum Sq Mean Sq F value Pr(>F)
## factor(x$race) 3 7657 2552.21 31.813 < 2.2e-16 ***
## Residuals 796 63859 80.22
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $math
## Analysis of Variance Table
##
## Response: x$values
## Df Sum Sq Mean Sq F value Pr(>F)
## factor(x$race) 3 7369 2456.19 31.285 < 2.2e-16 ***
## Residuals 796 62495 78.51
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $science
## Analysis of Variance Table
##
## Response: x$values
## Df Sum Sq Mean Sq F value Pr(>F)
## factor(x$race) 3 12678 4226.0 53.074 < 2.2e-16 ***
## Residuals 776 61789 79.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## $socst
## Analysis of Variance Table
##
## Response: x$values
## Df Sum Sq Mean Sq F value Pr(>F)
## factor(x$race) 3 3776 1258.51 11.388 2.562e-07 ***
## Residuals 796 87969 110.51
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Ans：Different ethnic groups have the different mean scores on every subject.
(c) Perform all pairwise simple regressions for these variables: read, write, math, science, and socst.
read與write, math, science, socst的回歸
## id female race ses schtyp prog read write math science socst
## 1 70 male white low public general 57 52 41 47 57
## 2 121 female white middle public vocation 68 59 53 63 61
## 3 86 male white high public general 44 33 54 58 31
## 4 141 male white high public vocation 63 44 47 53 56
## 5 172 male white middle public academic 47 52 57 53 61
## 6 113 male white middle public academic 44 52 51 63 61read <- dta[,"read"]
read.1 <- lapply(dta[, 8:11], function(x) lm(read ~ x))
lapply(read.1[1:4], broom::tidy)## $write
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 18.2 3.31 5.49 1.21e- 7
## 2 x 0.646 0.0617 10.5 1.11e-20
##
## $math
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 14.1 3.12 4.52 1.08e- 5
## 2 x 0.725 0.0583 12.4 1.28e-26
##
## $science
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 18.2 3.10 5.87 1.91e- 8
## 2 x 0.654 0.0586 11.2 1.22e-22
##
## $socst
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 21.1 2.84 7.43 3.22e-12
## 2 x 0.594 0.0532 11.2 9.29e-23write與math, science, socst的回歸
write <- dta[,"write"]
write.1 <- lapply(dta[, 9:11], function(x) lm(write ~ x))
lapply(read.1[1:3], broom::tidy)## $write
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 18.2 3.31 5.49 1.21e- 7
## 2 x 0.646 0.0617 10.5 1.11e-20
##
## $math
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 14.1 3.12 4.52 1.08e- 5
## 2 x 0.725 0.0583 12.4 1.28e-26
##
## $science
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 18.2 3.10 5.87 1.91e- 8
## 2 x 0.654 0.0586 11.2 1.22e-22math與science, socst的回歸
math <- dta[,"math"]
math.1 <- lapply(dta[, 9:11], function(x) lm(math ~ x))
lapply(read.1[1:2], broom::tidy)## $write
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 18.2 3.31 5.49 1.21e- 7
## 2 x 0.646 0.0617 10.5 1.11e-20
##
## $math
## # A tibble: 2 x 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 14.1 3.12 4.52 1.08e- 5
## 2 x 0.725 0.0583 12.4 1.28e-26science與socst的回歸
##
## Call:
## lm(formula = science ~ socst, data = dta)
##
## Coefficients:
## (Intercept) socst
## 30.1197 0.4167