Multiple Regression with R, on IQ for Gini and Linguistic Diversity

Similar to the post about linear regression, Linear Regression with R, on IQ for Gini and Linguistc Diversity, this the same data used for multiple regression, with some minor but statistically significant examples:

Example Code

 # LM - Multiple Regression  

 # Load the data into a matrix  
 oecdData <- read.table("OECD - Quality of Life.csv", header = TRUE, sep = ",")  
 print(names(oecdData))  
 # Access the vectors  
 v1 <- oecdData$IQ  
 v2 <- oecdData$HofstederPowerDx  
 v3 <- oecdData$HofstederMasculinity  
 v4 <- oecdData$HofstederIndividuality  
 v5 <- oecdData$HofstederUncertaintyAvoidance  
 v6 <- oecdData$Diversity_Ethnic  
 v7 <- oecdData$Diversity_Linguistic  
 v8 <- oecdData$Diversity_Religious  
 v9 <- oecdData$Gini  

 # Gini ~ Hofstede  
 relation1 <- lm(v9 ~ v2 + v3 + v4 + v5)  
 print(relation1)  
 print(summary(relation1))  
 print(anova(relation1))  

 # IQ ~ Hofstede Individuality, Linguistic Diversity  
 relation1 <- lm(v1 ~ v4 + v7)  
 print(relation1)  
 print(summary(relation1))  
 print(anova(relation1))  

Example Results

 > # Load the data into a matrix   
 + oecdData <- read.table("OECD - Quality of Life.csv", header = TRUE, sep = ",")  
 +   
 + # Access the vectors   
 + v1 <- oecdData$IQ  
 + v2 <- oecdData$HofstederPowerDx  
 + v3 <- oecdData$HofstederMasculinity  
 + v4 <- oecdData$HofstederIndividuality  
 + v5 <- oecdData$HofstederUncertaintyAvoidance  
 + v6 <- oecdData$Diversity_Ethnic  
 + v7 <- oecdData$Diversity_Linguistic  
 + v8 <- oecdData$Diversity_Religious  
 + v9 <- oecdData$Gini  
 +   
 + # Gini ~ Hofstede   
 + relation1 <- lm(v9 ~ v2 + v3 + v4 + v5)  
 + print(relation1)  
 + print(summary(relation1))  
 + print(anova(relation1))  
 +   
 + # IQ ~ Hofstede Individuality, Linguistic Diversity   
 + relation1 <- lm(v1 ~ v4 + v7)  
 + print(relation1)  
 + print(summary(relation1))  
 + print(anova(relation1))  
   
 Call:  
 lm(formula = v9 ~ v2 + v3 + v4 + v5)  
   
 Coefficients:  
 (Intercept)      v2      v3      v4      v5   
   25.87750   0.10809   0.07172   0.01641   -0.04880   
   
   
 Call:  
 lm(formula = v9 ~ v2 + v3 + v4 + v5)  
   
 Residuals:  
   Min   1Q Median   3Q   Max   
 -9.8929 -2.6618 0.2999 2.5365 8.2216   
   
 Coefficients:  
       Estimate Std. Error t value Pr(>|t|)    
 (Intercept) 25.87750  8.36212  3.095 0.00658 **  
 v2      0.10809  0.12080  0.895 0.38342    
 v3      0.07172  0.05201  1.379 0.18582    
 v4      0.01641  0.08473  0.194 0.84871    
 v5     -0.04880  0.10407 -0.469 0.64509    
 ---  
 Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  
   
 Residual standard error: 4.967 on 17 degrees of freedom  
  (3 observations deleted due to missingness)  
 Multiple R-squared: 0.1497,     Adjusted R-squared: -0.05035   
 F-statistic: 0.7483 on 4 and 17 DF, p-value: 0.5726  
   
 Analysis of Variance Table  
   
 Response: v9  
      Df Sum Sq Mean Sq F value Pr(>F)  
 v2     1 10.28 10.277 0.4166 0.5273  
 v3     1 45.83 45.827 1.8577 0.1907  
 v4     1 12.31 12.312 0.4991 0.4895  
 v5     1  5.42  5.424 0.2199 0.6451  
 Residuals 17 419.36 24.668          
   
 Call:  
 lm(formula = v1 ~ v4 + v7)  
   
 Coefficients:  
 (Intercept)      v4      v7   
  100.21289   -0.02029   1.78454   
   
   
 Call:  
 lm(formula = v1 ~ v4 + v7)  
   
 Residuals:  
   Min   1Q Median   3Q   Max   
 -7.5562 -1.2709 -0.2722 2.3429 6.1523   
   
 Coefficients:  
        Estimate Std. Error t value Pr(>|t|)    
 (Intercept) 100.21289  2.74669 36.485  <2e-16 ***  
 v4      -0.02029  0.04525 -0.448  0.659    
 v7      1.78454  4.33483  0.412  0.685    
 ---  
 Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  
   
 Residual standard error: 3.563 on 19 degrees of freedom  
  (3 observations deleted due to missingness)  
 Multiple R-squared: 0.01297,     Adjusted R-squared: -0.09093   
 F-statistic: 0.1248 on 2 and 19 DF, p-value: 0.8834  
   
 Analysis of Variance Table  
   
 Response: v1  
      Df  Sum Sq Mean Sq F value Pr(>F)  
 v4     1  1.018  1.0175  0.0802  0.7802  
 v7     1  2.151  2.1514  0.1695  0.6852  
 Residuals 19 241.195 12.6945          
 >   

Example Plot

Sample Data