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setwd("~")
winequality <- read.csv("winequality-red.csv",header=TRUE)
names(winequality)
##  [1] "fixed.acidity"        "volatile.acidity"     "citric.acid"         
##  [4] "residual.sugar"       "chlorides"            "free.sulfur.dioxide" 
##  [7] "total.sulfur.dioxide" "density"              "pH"                  
## [10] "sulphates"            "alcohol"              "quality"
head(winequality)
##   fixed.acidity volatile.acidity citric.acid residual.sugar chlorides
## 1           7.4             0.70        0.00            1.9     0.076
## 2           7.8             0.88        0.00            2.6     0.098
## 3           7.8             0.76        0.04            2.3     0.092
## 4          11.2             0.28        0.56            1.9     0.075
## 5           7.4             0.70        0.00            1.9     0.076
## 6           7.4             0.66        0.00            1.8     0.075
##   free.sulfur.dioxide total.sulfur.dioxide density   pH sulphates alcohol
## 1                  11                   34  0.9978 3.51      0.56     9.4
## 2                  25                   67  0.9968 3.20      0.68     9.8
## 3                  15                   54  0.9970 3.26      0.65     9.8
## 4                  17                   60  0.9980 3.16      0.58     9.8
## 5                  11                   34  0.9978 3.51      0.56     9.4
## 6                  13                   40  0.9978 3.51      0.56     9.4
##   quality
## 1       5
## 2       5
## 3       5
## 4       6
## 5       5
## 6       5
summary(winequality)
##  fixed.acidity   volatile.acidity  citric.acid    residual.sugar  
##  Min.   : 4.60   Min.   :0.1200   Min.   :0.000   Min.   : 0.900  
##  1st Qu.: 7.10   1st Qu.:0.3900   1st Qu.:0.090   1st Qu.: 1.900  
##  Median : 7.90   Median :0.5200   Median :0.260   Median : 2.200  
##  Mean   : 8.32   Mean   :0.5278   Mean   :0.271   Mean   : 2.539  
##  3rd Qu.: 9.20   3rd Qu.:0.6400   3rd Qu.:0.420   3rd Qu.: 2.600  
##  Max.   :15.90   Max.   :1.5800   Max.   :1.000   Max.   :15.500  
##    chlorides       free.sulfur.dioxide total.sulfur.dioxide
##  Min.   :0.01200   Min.   : 1.00       Min.   :  6.00      
##  1st Qu.:0.07000   1st Qu.: 7.00       1st Qu.: 22.00      
##  Median :0.07900   Median :14.00       Median : 38.00      
##  Mean   :0.08747   Mean   :15.87       Mean   : 46.47      
##  3rd Qu.:0.09000   3rd Qu.:21.00       3rd Qu.: 62.00      
##  Max.   :0.61100   Max.   :72.00       Max.   :289.00      
##     density             pH          sulphates         alcohol     
##  Min.   :0.9901   Min.   :2.740   Min.   :0.3300   Min.   : 8.40  
##  1st Qu.:0.9956   1st Qu.:3.210   1st Qu.:0.5500   1st Qu.: 9.50  
##  Median :0.9968   Median :3.310   Median :0.6200   Median :10.20  
##  Mean   :0.9967   Mean   :3.311   Mean   :0.6581   Mean   :10.42  
##  3rd Qu.:0.9978   3rd Qu.:3.400   3rd Qu.:0.7300   3rd Qu.:11.10  
##  Max.   :1.0037   Max.   :4.010   Max.   :2.0000   Max.   :14.90  
##     quality     
##  Min.   :3.000  
##  1st Qu.:5.000  
##  Median :6.000  
##  Mean   :5.636  
##  3rd Qu.:6.000  
##  Max.   :8.000
plot(winequality)

plot(winequality$density,winequality$fixed.acidity)

plot(winequality$fixed.acidity,winequality$pH)

hist(winequality$density)

hist(winequality$chlorides)

hist(winequality$pH)

boxplot(winequality$density)

boxplot(winequality$chlorides)

cor(winequality$density,winequality$fixed.acidity)
## [1] 0.6680473
cor(winequality$pH,winequality$fixed.acidity)
## [1] -0.6829782
lm(formula = quality ~ density + pH + fixed.acidity, data = winequality)
## 
## Call:
## lm(formula = quality ~ density + pH + fixed.acidity, data = winequality)
## 
## Coefficients:
##   (Intercept)        density             pH  fixed.acidity  
##      213.1960      -213.1606         0.8242         0.2618
cor.test(winequality$pH,winequality$fixed.acidity)
## 
##  Pearson's product-moment correlation
## 
## data:  winequality$pH and winequality$fixed.acidity
## t = -37.3659, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.7082857 -0.6559174
## sample estimates:
##        cor 
## -0.6829782
cor.test(winequality$density,winequality$fixed.acidity)
## 
##  Pearson's product-moment correlation
## 
## data:  winequality$density and winequality$fixed.acidity
## t = 35.8771, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6399847 0.6943302
## sample estimates:
##       cor 
## 0.6680473
attach(winequality)
model1<-lm(quality~fixed.acidity+residual.sugar+total.sulfur.dioxide+sulphates+volatile.acidity+chlorides+density+alcohol+citric.acid+free.sulfur.dioxide+pH)
detach(winequality)
model1
## 
## Call:
## lm(formula = quality ~ fixed.acidity + residual.sugar + total.sulfur.dioxide + 
##     sulphates + volatile.acidity + chlorides + density + alcohol + 
##     citric.acid + free.sulfur.dioxide + pH)
## 
## Coefficients:
##          (Intercept)         fixed.acidity        residual.sugar  
##            21.965208              0.024991              0.016331  
## total.sulfur.dioxide             sulphates      volatile.acidity  
##            -0.003265              0.916334             -1.083590  
##            chlorides               density               alcohol  
##            -1.874225            -17.881164              0.276198  
##          citric.acid   free.sulfur.dioxide                    pH  
##            -0.182564              0.004361             -0.413653
summary(model1)
## 
## Call:
## lm(formula = quality ~ fixed.acidity + residual.sugar + total.sulfur.dioxide + 
##     sulphates + volatile.acidity + chlorides + density + alcohol + 
##     citric.acid + free.sulfur.dioxide + pH)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.68911 -0.36652 -0.04699  0.45202  2.02498 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           2.197e+01  2.119e+01   1.036   0.3002    
## fixed.acidity         2.499e-02  2.595e-02   0.963   0.3357    
## residual.sugar        1.633e-02  1.500e-02   1.089   0.2765    
## total.sulfur.dioxide -3.265e-03  7.287e-04  -4.480 8.00e-06 ***
## sulphates             9.163e-01  1.143e-01   8.014 2.13e-15 ***
## volatile.acidity     -1.084e+00  1.211e-01  -8.948  < 2e-16 ***
## chlorides            -1.874e+00  4.193e-01  -4.470 8.37e-06 ***
## density              -1.788e+01  2.163e+01  -0.827   0.4086    
## alcohol               2.762e-01  2.648e-02  10.429  < 2e-16 ***
## citric.acid          -1.826e-01  1.472e-01  -1.240   0.2150    
## free.sulfur.dioxide   4.361e-03  2.171e-03   2.009   0.0447 *  
## pH                   -4.137e-01  1.916e-01  -2.159   0.0310 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared:  0.3606, Adjusted R-squared:  0.3561 
## F-statistic: 81.35 on 11 and 1587 DF,  p-value: < 2.2e-16

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