HW7.Rmd

---
title: "S631 HW7"
author: "Wencao Yang"
date: "10/21/2016"
output: html_document
---

#1 ALR4 problem 4.5
The regression coefficient is the percentage change in Y.If use log(Y) as response, the coefficient will be responding to a percentage change of log(Y) and then the exponential change of Y 

#2 ALR4 problem 4.6
```{r}
library(alr4)
head(UN11)
m0=lm(log(fertility)~pctUrban,data=UN11)
plot(log(fertility)~pctUrban,data = UN11)
abline(m0)
```

intercept of 1.501 means the log(fertility) when percentage of Urban is 0 and slope of 0.01 means that every 1 percentage increase of Urban rate decrease log(fertility) by 0.01.

#3 ALR4 problem 4.9

## 4.9.1
intercept of 24697 is the estimated salary for male and slope of 3340 is the part of salary female faculty earn less than male faculty.

## 4.9.2
Because sex and years are not completely independent or dependent.

#4 ALR4 problem 5.17.1 to 5.17.3
```{r}
head(salary)
scatterplotMatrix(~salary+degree+rank+sex+year+ysdeg,data = salary)
m1=lm(salary~degree+rank+sex+year+ysdeg,data = salary)
summary(m1)
salarymen<-subset(salary,sex=='Male')
salarywomen<-subset(salary,sex=='Female')
t.test(salarymen$salary,salarywomen$salary)
```

salary increases with rank and year, almost independent of degree, slight difference for different sex

We cannot reject the null hypothesis,i.e., the salary for men and women is the same.Alternative hypothesis is mean salary for men and women is different.

Finally, the 95% confidence interval for the difference of salary for men and women is (-567.8539,7247.1471)