Bordeaux is a region in France popular for producing wine. While this wine has been produced in much the same way for hundreds of years, there are differences in price and quality from year to year that are sometimes very significant. Bordeaux wines are widely believed to taste better when they are older, so there’s an incentive to store young wines until they are mature. The main problem is that it is hard to determine the quality of the wine when it is so young just by tasting it,since the taste will change so significantly by the time it will actually be consumed. This is why wine tasters and experts are helpful. They taste the wines and then predict which ones will be the best wines later. The question we’ll address in this lecture– can analytics model this process better and make stronger predictions?
setwd("C:/Users/jzchen/Documents/Courses/Analytics edge/Unit 2")
wine <- read.csv("wine.csv")
str(wine)## 'data.frame': 25 obs. of 7 variables:
## $ Year : int 1952 1953 1955 1957 1958 1959 1960 1961 1962 1963 ...
## $ Price : num 7.5 8.04 7.69 6.98 6.78 ...
## $ WinterRain : int 600 690 502 420 582 485 763 830 697 608 ...
## $ AGST : num 17.1 16.7 17.1 16.1 16.4 ...
## $ HarvestRain: int 160 80 130 110 187 187 290 38 52 155 ...
## $ Age : int 31 30 28 26 25 24 23 22 21 20 ...
## $ FrancePop : num 43184 43495 44218 45152 45654 ...model1 <- lm(Price ~ AGST, data = wine)
summary(model1)##
## Call:
## lm(formula = Price ~ AGST, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.78450 -0.23882 -0.03727 0.38992 0.90318
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.4178 2.4935 -1.371 0.183710
## AGST 0.6351 0.1509 4.208 0.000335 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4993 on 23 degrees of freedom
## Multiple R-squared: 0.435, Adjusted R-squared: 0.4105
## F-statistic: 17.71 on 1 and 23 DF, p-value: 0.000335model1$residuals## 1 2 3 4 5 6
## 0.04204258 0.82983774 0.21169394 0.15609432 -0.23119140 0.38991701
## 7 8 9 10 11 12
## -0.48959140 0.90318115 0.45372410 0.14887461 -0.23882157 -0.08974238
## 13 14 15 16 17 18
## 0.66185660 -0.05211511 -0.62726647 -0.74714947 0.42113502 -0.03727441
## 19 20 21 22 23 24
## 0.10685278 -0.78450270 -0.64017590 -0.05508720 -0.67055321 -0.22040381
## 25
## 0.55866518SSE <- sum(model1$residuals^2)
SSE## [1] 5.734875model2 <- lm(Price ~ AGST + HarvestRain, data = wine)
summary(model2)##
## Call:
## lm(formula = Price ~ AGST + HarvestRain, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.88321 -0.19600 0.06178 0.15379 0.59722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.20265 1.85443 -1.188 0.247585
## AGST 0.60262 0.11128 5.415 1.94e-05 ***
## HarvestRain -0.00457 0.00101 -4.525 0.000167 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3674 on 22 degrees of freedom
## Multiple R-squared: 0.7074, Adjusted R-squared: 0.6808
## F-statistic: 26.59 on 2 and 22 DF, p-value: 1.347e-06model2$residuals## 1 2 3 4 5
## 0.114049616 0.523788530 0.147680820 -0.032339673 -0.058527063
## 6 7 8 9 10
## 0.597221745 0.153788612 0.424676073 0.005640893 0.152563009
## 11 12 13 14 15
## -0.454426446 0.414425096 0.376732242 -0.200740923 0.018215806
## 16 17 18 19 20
## -0.309662756 0.154053312 -0.195997112 0.100432413 -0.883211577
## 21 22 23 24 25
## -0.485011835 0.061776460 -0.183631188 -0.531811642 0.090315589SSE2 <- sum(model2$residuals^2)
SSE2## [1] 2.970373Note that in practice, we don’t care about the SSE on the training set.
model3 <- lm(Price ~ AGST + HarvestRain + WinterRain + Age + FrancePop, data = wine)
summary(model3)##
## Call:
## lm(formula = Price ~ AGST + HarvestRain + WinterRain + Age +
## FrancePop, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.48179 -0.24662 -0.00726 0.22012 0.51987
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.504e-01 1.019e+01 -0.044 0.965202
## AGST 6.012e-01 1.030e-01 5.836 1.27e-05 ***
## HarvestRain -3.958e-03 8.751e-04 -4.523 0.000233 ***
## WinterRain 1.043e-03 5.310e-04 1.963 0.064416 .
## Age 5.847e-04 7.900e-02 0.007 0.994172
## FrancePop -4.953e-05 1.667e-04 -0.297 0.769578
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3019 on 19 degrees of freedom
## Multiple R-squared: 0.8294, Adjusted R-squared: 0.7845
## F-statistic: 18.47 on 5 and 19 DF, p-value: 1.044e-06SSE3 <- sum(model3$residuals^2)
SSE3## [1] 1.732113model4 <- lm(Price ~ HarvestRain + WinterRain, data = wine)
summary(model4)##
## Call:
## lm(formula = Price ~ HarvestRain + WinterRain, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0933 -0.3222 -0.1012 0.3871 1.1877
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.865e+00 6.616e-01 11.888 4.76e-11 ***
## HarvestRain -4.971e-03 1.601e-03 -3.105 0.00516 **
## WinterRain -9.848e-05 9.007e-04 -0.109 0.91392
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5611 on 22 degrees of freedom
## Multiple R-squared: 0.3177, Adjusted R-squared: 0.2557
## F-statistic: 5.122 on 2 and 22 DF, p-value: 0.01492model4 <- lm(Price ~ AGST + HarvestRain + WinterRain + Age, data = wine)
summary(model4)##
## Call:
## lm(formula = Price ~ AGST + HarvestRain + WinterRain + Age, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.45470 -0.24273 0.00752 0.19773 0.53637
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.4299802 1.7658975 -1.942 0.066311 .
## AGST 0.6072093 0.0987022 6.152 5.2e-06 ***
## HarvestRain -0.0039715 0.0008538 -4.652 0.000154 ***
## WinterRain 0.0010755 0.0005073 2.120 0.046694 *
## Age 0.0239308 0.0080969 2.956 0.007819 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.295 on 20 degrees of freedom
## Multiple R-squared: 0.8286, Adjusted R-squared: 0.7943
## F-statistic: 24.17 on 4 and 20 DF, p-value: 2.036e-07model5 <- lm(Price ~ HarvestRain + WinterRain, data = wine)
summary(model5)##
## Call:
## lm(formula = Price ~ HarvestRain + WinterRain, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0933 -0.3222 -0.1012 0.3871 1.1877
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.865e+00 6.616e-01 11.888 4.76e-11 ***
## HarvestRain -4.971e-03 1.601e-03 -3.105 0.00516 **
## WinterRain -9.848e-05 9.007e-04 -0.109 0.91392
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5611 on 22 degrees of freedom
## Multiple R-squared: 0.3177, Adjusted R-squared: 0.2557
## F-statistic: 5.122 on 2 and 22 DF, p-value: 0.01492If we compare 5th model to 3rd model, we will see that after removing FranceProp, Age becomes a more significant variable in the new model, while before it was not at all.
cor(wine$WinterRain, wine$Price)## [1] 0.1366505cor(wine$Age, wine$FrancePop)## [1] -0.9944851cor(wine)## Year Price WinterRain AGST HarvestRain
## Year 1.00000000 -0.4477679 0.016970024 -0.24691585 0.02800907
## Price -0.44776786 1.0000000 0.136650547 0.65956286 -0.56332190
## WinterRain 0.01697002 0.1366505 1.000000000 -0.32109061 -0.27544085
## AGST -0.24691585 0.6595629 -0.321090611 1.00000000 -0.06449593
## HarvestRain 0.02800907 -0.5633219 -0.275440854 -0.06449593 1.00000000
## Age -1.00000000 0.4477679 -0.016970024 0.24691585 -0.02800907
## FrancePop 0.99448510 -0.4668616 -0.001621627 -0.25916227 0.04126439
## Age FrancePop
## Year -1.00000000 0.994485097
## Price 0.44776786 -0.466861641
## WinterRain -0.01697002 -0.001621627
## AGST 0.24691585 -0.259162274
## HarvestRain -0.02800907 0.041264394
## Age 1.00000000 -0.994485097
## FrancePop -0.99448510 1.000000000Remove both age and france population from the model
model5 <- lm(Price ~ AGST + HarvestRain + WinterRain, data = wine)
summary(model5)##
## Call:
## lm(formula = Price ~ AGST + HarvestRain + WinterRain, data = wine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.67472 -0.12958 0.01973 0.20751 0.63846
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.3016263 2.0366743 -2.112 0.046831 *
## AGST 0.6810242 0.1117011 6.097 4.75e-06 ***
## HarvestRain -0.0039481 0.0009987 -3.953 0.000726 ***
## WinterRain 0.0011765 0.0005920 1.987 0.060097 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.345 on 21 degrees of freedom
## Multiple R-squared: 0.7537, Adjusted R-squared: 0.7185
## F-statistic: 21.42 on 3 and 21 DF, p-value: 1.359e-06R squared dropped. Model4 remains to be a better model.
wineTest <- read.csv("wine_test.csv")
str(wineTest)## 'data.frame': 2 obs. of 7 variables:
## $ Year : int 1979 1980
## $ Price : num 6.95 6.5
## $ WinterRain : int 717 578
## $ AGST : num 16.2 16
## $ HarvestRain: int 122 74
## $ Age : int 4 3
## $ FrancePop : num 54836 55110predictTest <- predict(model4, newdata = wineTest)
predictTest## 1 2
## 6.768925 6.684910SSE <- sum((wineTest$Price - predictTest)^2)
SST <- sum((wineTest$Price - mean(wine$Price))^2)
1 - SSE/SST## [1] 0.7944278