Kapitel 4

av Erik och Tobbe

Prob 4.03

require(mosaic)
swim = fetchData("SwimRecords")

a)

• Mean = 65.2
• Min = 53.5

timeWomen = subset(swim, sex == "F")
mean(time, data = timeWomen)

## [1] 65.19

min(time, data = timeWomen)

## [1] 53.52

b)

• Mean = 73.8
• Min = 61.4

recordsBefore1920 = subset(swim, year < 1920)
mean(time, data = recordsBefore1920)

## [1] 73.84

min(time, data = recordsBefore1920)

## [1] 61.4

c)

• Mean = 69.6
• Min = 60.2

slowerThan60 = subset(swim, time > 60)
mean(time, data = slowerThan60)

## [1] 69.62

min(time, data = slowerThan60)

## [1] 60.2

Prob 4.04

mod = mm(wage ~ sector, data = CPS85)

a)

9.50 Eftersom mm() ger medelvärdet för wage uppdelat i sektor så står svaret att finna i tabellen.

mod

## 
## Groupwise Model Call:
## wage ~ sector
## 
## Coefficients:
## clerical     const     manag     manuf     other      prof     sales  
##     7.42      9.50     12.70      8.04      8.50     11.95      7.59  
##  service  
##     6.54

b)

12.70 Eftersom mm() ger medelvärdet för wage uppdelat i sektor så står svaret att finna i tabellen.

mod

## 
## Groupwise Model Call:
## wage ~ sector
## 
## Coefficients:
## clerical     const     manag     manuf     other      prof     sales  
##     7.42      9.50     12.70      8.04      8.50     11.95      7.59  
##  service  
##     6.54

c)

service (6.53)

min(fitted(mod))

## [1] 6.537

d)

2.20

sd(fitted(mod))

## [1] 2.197

e)

4.65

sd(resid(mod))

## [1] 4.646

Prob 4.05

mod1 = mm(wage ~ 1, data = CPS85)
mod2 = mm(wage ~ sector, data = CPS85)

a)

mod2

var(fitted(mod1))

## [1] 0

var(fitted(mod2))

## [1] 4.825

b)

mod1

var(resid(mod1))

## [1] 26.41

var(resid(mod2))

## [1] 21.59

c)

Tredje punkten eftersom det är varians som unikt har den egenskapen.

Prob 4.06

w = fetchData("CPS85")

a)

9.02

mm(wage ~ 1, data = w)

## 
## Groupwise Model Call:
## wage ~ 1
## 
## Coefficients:
##  all  
## 9.02

b)

7.88

mm(wage ~ 1, data = subset(w, sex == "F"))

## 
## Groupwise Model Call:
## wage ~ 1
## 
## Coefficients:
##  all  
## 7.88

c)

9.40

mm(wage ~ 1, data = subset(w, married == "Married"))

## 
## Groupwise Model Call:
## wage ~ 1
## 
## Coefficients:
## all  
## 9.4

d)

7.68

mm(wage ~ 1, data = subset(w, married == "Married" & sex == "F"))

## 
## Groupwise Model Call:
## wage ~ 1
## 
## Coefficients:
##  all  
## 7.68

Prob 4.07

g = fetchData("Galton")

a)

3.58

sd(height, data = g)

## [1] 3.583

b)

3.58

mod0 = mm(height ~ 1, data = g)
res = resid(mod0)

sd(res)

## [1] 3.583

c)

2.51

mod1 = mm(height ~ sex, data = g)
res1 = resid(mod1)

sd(res)

## [1] 3.583

d)

mod1 (2.51 < 3.58)