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
Example Results
Example Plot
Sample Data
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
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