Regression Model and Model Fit (Adjusted R-squared)
mymodel_0 <- lm(quality~pH+residual.sugar+fixed.acidity*alcohol, data=wine_dataset)
summary(mymodel_0)
##
## Call:
## lm(formula = quality ~ pH + residual.sugar + fixed.acidity *
## alcohol, data = wine_dataset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7470 -0.4027 -0.1116 0.5089 2.5206
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.360170 0.900184 2.622 0.008828 **
## pH -0.558337 0.159099 -3.509 0.000462 ***
## residual.sugar -0.014286 0.012489 -1.144 0.252841
## fixed.acidity 0.143758 0.087747 1.638 0.101552
## alcohol 0.461324 0.068569 6.728 2.39e-11 ***
## fixed.acidity:alcohol -0.009741 0.008161 -1.194 0.232832
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6971 on 1593 degrees of freedom
## Multiple R-squared: 0.2571, Adjusted R-squared: 0.2548
## F-statistic: 110.3 on 5 and 1593 DF, p-value: < 2.2e-16
Correlation Analysis and Test
cor(wine_dataset$pH,wine_dataset$quality)
## [1] -0.05773139
cor(wine_dataset$alcohol,wine_dataset$quality)
## [1] 0.4761663
cor(wine_dataset$residual.sugar,wine_dataset$quality)
## [1] 0.01373164
cor(wine_dataset$fixed.acidity,wine_dataset$quality)
## [1] 0.1240516
cor.test(wine_dataset$pH,wine_dataset$quality)
##
## Pearson's product-moment correlation
##
## data: wine_dataset$pH and wine_dataset$quality
## t = -2.3109, df = 1597, p-value = 0.02096
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.106451268 -0.008734972
## sample estimates:
## cor
## -0.05773139
cor.test(wine_dataset$alcohol,wine_dataset$quality)
##
## Pearson's product-moment correlation
##
## data: wine_dataset$alcohol and wine_dataset$quality
## t = 21.639, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4373540 0.5132081
## sample estimates:
## cor
## 0.4761663
cor.test(wine_dataset$residual.sugar,wine_dataset$quality)
##
## Pearson's product-moment correlation
##
## data: wine_dataset$residual.sugar and wine_dataset$quality
## t = 0.5488, df = 1597, p-value = 0.5832
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.03531327 0.06271056
## sample estimates:
## cor
## 0.01373164
cor.test(wine_dataset$fixed.acidity,wine_dataset$quality)
##
## Pearson's product-moment correlation
##
## data: wine_dataset$fixed.acidity and wine_dataset$quality
## t = 4.996, df = 1597, p-value = 6.496e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07548957 0.17202667
## sample estimates:
## cor
## 0.1240516
Assumptions
hist(mymodel_0$residuals)

plot(mymodel_0$fitted.values,mymodel_0$residuals)
abline(h=0, col='red')

vif(mymodel_0)
## pH residual.sugar fixed.acidity
## 1.983798 1.019477 76.745904
## alcohol fixed.acidity:alcohol
## 17.556829 89.125755