HHernandez_DATA621_Discussion06

LMR Exercise 7.3

require("faraway")
require("ggplot2")

data("divusa")
summary(divusa)

##       year         divorce        unemployed         femlab     
##  Min.   :1920   Min.   : 6.10   Min.   : 1.200   Min.   :22.70  
##  1st Qu.:1939   1st Qu.: 8.70   1st Qu.: 4.200   1st Qu.:27.47  
##  Median :1958   Median :10.60   Median : 5.600   Median :37.10  
##  Mean   :1958   Mean   :13.27   Mean   : 7.173   Mean   :38.58  
##  3rd Qu.:1977   3rd Qu.:20.30   3rd Qu.: 7.500   3rd Qu.:47.80  
##  Max.   :1996   Max.   :22.80   Max.   :24.900   Max.   :59.30  
##     marriage          birth           military     
##  Min.   : 49.70   Min.   : 65.30   Min.   : 1.940  
##  1st Qu.: 61.90   1st Qu.: 68.90   1st Qu.: 3.469  
##  Median : 74.10   Median : 85.90   Median : 9.102  
##  Mean   : 72.97   Mean   : 88.89   Mean   :12.365  
##  3rd Qu.: 80.00   3rd Qu.:107.30   3rd Qu.:14.266  
##  Max.   :118.10   Max.   :122.90   Max.   :86.641

# Fit model 1
l_mod <- lm(divorce ~ .-year, data = divusa)
summary(l_mod)

## 
## Call:
## lm(formula = divorce ~ . - year, data = divusa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8611 -0.8916 -0.0496  0.8650  3.8300 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.48784    3.39378   0.733   0.4659    
## unemployed  -0.11125    0.05592  -1.989   0.0505 .  
## femlab       0.38365    0.03059  12.543  < 2e-16 ***
## marriage     0.11867    0.02441   4.861 6.77e-06 ***
## birth       -0.12996    0.01560  -8.333 4.03e-12 ***
## military    -0.02673    0.01425  -1.876   0.0647 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.65 on 71 degrees of freedom
## Multiple R-squared:  0.9208, Adjusted R-squared:  0.9152 
## F-statistic: 165.1 on 5 and 71 DF,  p-value: < 2.2e-16

round(cor(divusa[,-1]),2)

##            divorce unemployed femlab marriage birth military
## divorce       1.00      -0.21   0.91    -0.53 -0.72     0.02
## unemployed   -0.21       1.00  -0.26    -0.27 -0.31    -0.40
## femlab        0.91      -0.26   1.00    -0.65 -0.60     0.05
## marriage     -0.53      -0.27  -0.65     1.00  0.67     0.26
## birth        -0.72      -0.31  -0.60     0.67  1.00     0.14
## military      0.02      -0.40   0.05     0.26  0.14     1.00

x <- model.matrix(l_mod)[,-1]
vif(x)

## unemployed     femlab   marriage      birth   military 
##   2.252888   3.613276   2.864864   2.585485   1.249596

# Fit model 2 (removal of insignificant predictors)
l_mod2 <- lm(divorce ~ .-year -unemployed - military, data = divusa)
summary(l_mod2)

## 
## Call:
## lm(formula = divorce ~ . - year - unemployed - military, data = divusa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6923 -1.1934 -0.0534  1.2265  3.6701 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.54545    2.21247  -0.699    0.487    
## femlab       0.41337    0.02275  18.174  < 2e-16 ***
## marriage     0.12609    0.02199   5.735 2.07e-07 ***
## birth       -0.11627    0.01412  -8.235 5.10e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.695 on 73 degrees of freedom
## Multiple R-squared:  0.9141, Adjusted R-squared:  0.9106 
## F-statistic: 258.9 on 3 and 73 DF,  p-value: < 2.2e-16

x <- model.matrix(l_mod2)[,-1]
vif(x)

##   femlab marriage    birth 
## 1.893390 2.201891 2.008469