0.1 Open data

#file location
fL<-"https://math.montana.edu/shancock/data/Framingham.txt"
dta <- read.table(fL, header=T)

0.2 recode gender variable

# 
dta$sex <- factor(dta$sex, 
                  levels=c(1, 2), 
                  labels=c("M", "F"))

0.3 lattice plot

library(lattice)
xyplot(sbp ~ dbp | sex, 
       data=dta, cex=.5,
       type=c("p","g","r"),
       xlab="Diastolic pressure (mmHg)",
       ylab="Systolic pressure (mmHg)")

0.4 regression

m0 <- lm(sbp ~ dbp, data=dta)
m1 <- lm(sbp ~ dbp + sex, data=dta)
m2 <- lm(sbp ~ dbp + sex + sex:dbp, data=dta)

#compare 3 model
anova(m0, m1, m2)
## Analysis of Variance Table
## 
## Model 1: sbp ~ dbp
## Model 2: sbp ~ dbp + sex
## Model 3: sbp ~ dbp + sex + sex:dbp
##   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
## 1   4697 941778                                  
## 2   4696 927853  1     13925 71.800 < 2.2e-16 ***
## 3   4695 910543  1     17310 89.256 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(m2)
## 
## Call:
## lm(formula = sbp ~ dbp + sex + sex:dbp, data = dta)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.540  -8.990  -1.929   7.135  93.644 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  29.85394    2.14394  13.925  < 2e-16 ***
## dbp           1.22513    0.02542  48.198  < 2e-16 ***
## sexF        -22.10059    2.73844  -8.070 8.82e-16 ***
## dbp:sexF      0.30885    0.03269   9.448  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.93 on 4695 degrees of freedom
## Multiple R-squared:  0.6272, Adjusted R-squared:  0.627 
## F-statistic:  2633 on 3 and 4695 DF,  p-value: < 2.2e-16

0.5 plot

plot(rstandard(m2) ~ fitted(m2), 
     cex=.5, 
     xlab="Fitted values", 
     ylab="Standardized residuals")
grid()

0.6 The end

The results show ‘dbp:sex’ is significant, hence, sex in dbp and sbp have different fix effect.And the female slope is higher than male.