Projekt 2. dio
Tim 5: Jure Marinov, Marija Vugrinec, Lana Zebić, Dominik Žatečki
Podaci
data1 <- read.delim("realestate.txt")
data2 <- read_excel("Dry_Bean_Dataset.xlsx") |> mutate(Class = factor(Class))
data3 <- read_excel("kreditnekartice.xlsx")
realestate <- lm(SalesPrice ~ ., data = data1)
realestate2 <- lm(SalesPrice ~ SqFeet+Quality+Baths, data = data1)
realestate3 <- lm(SalesPrice ~ Beds+Garage+Year, data = data1)
realestate_aug <- augment(realestate)Multipla regresija
Deskriptivna analiza
data1 |> summary()## SalesPrice SqFeet Beds Baths
## Min. : 84.0 Min. :0.980 Min. :1.000 Min. :1.000
## 1st Qu.:180.0 1st Qu.:1.701 1st Qu.:3.000 1st Qu.:2.000
## Median :229.9 Median :2.061 Median :3.000 Median :3.000
## Mean :277.4 Mean :2.261 Mean :3.478 Mean :2.647
## 3rd Qu.:335.0 3rd Qu.:2.638 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :920.0 Max. :5.032 Max. :7.000 Max. :7.000
## AirCond Garage Pool Year
## Min. :0.0000 Min. :0.000 Min. :0.0000 Min. :1885
## 1st Qu.:1.0000 1st Qu.:2.000 1st Qu.:0.0000 1st Qu.:1956
## Median :1.0000 Median :2.000 Median :0.0000 Median :1966
## Mean :0.8311 Mean :2.098 Mean :0.0691 Mean :1967
## 3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.:0.0000 3rd Qu.:1981
## Max. :1.0000 Max. :7.000 Max. :1.0000 Max. :1998
## Quality Style Lot Highway
## Min. :1.000 Min. : 1.000 Min. : 4.56 Min. :0.00000
## 1st Qu.:2.000 1st Qu.: 1.000 1st Qu.:17.16 1st Qu.:0.00000
## Median :2.000 Median : 2.000 Median :22.20 Median :0.00000
## Mean :2.186 Mean : 3.349 Mean :24.34 Mean :0.02111
## 3rd Qu.:3.000 3rd Qu.: 7.000 3rd Qu.:26.78 3rd Qu.:0.00000
## Max. :3.000 Max. :11.000 Max. :86.83 Max. :1.00000summary(realestate)##
## Call:
## lm(formula = SalesPrice ~ ., data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -186.25 -37.55 -2.36 31.70 293.79
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2351.8910 433.9996 -5.419 9.26e-08 ***
## SqFeet 129.7452 7.6675 16.921 < 2e-16 ***
## Beds -8.2357 3.5350 -2.330 0.0202 *
## Baths 4.7172 4.6687 1.010 0.3128
## AirCond -13.5533 8.5834 -1.579 0.1150
## Garage 13.5320 5.4562 2.480 0.0135 *
## Pool 8.8900 11.2356 0.791 0.4292
## Year 1.2410 0.2188 5.671 2.38e-08 ***
## Quality -46.6914 7.4423 -6.274 7.54e-10 ***
## Style -9.4818 1.4305 -6.628 8.66e-11 ***
## Lot 1.1536 0.2579 4.473 9.51e-06 ***
## Highway -37.4620 19.6072 -1.911 0.0566 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 63.41 on 509 degrees of freedom
## Multiple R-squared: 0.7922, Adjusted R-squared: 0.7877
## F-statistic: 176.4 on 11 and 509 DF, p-value: < 2.2e-16glance(realestate)## # A tibble: 1 × 12
## r.squared adj.r.squ…¹ sigma stati…² p.value df logLik AIC BIC devia…³
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.792 0.788 63.4 176. 1.05e-165 11 -2895. 5816. 5872. 2.05e6
## # … with 2 more variables: df.residual <int>, nobs <int>, and abbreviated
## # variable names ¹adj.r.squared, ²statistic, ³devianceggplot(data = data1) +
aes(x = SqFeet) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(data = data1) +
aes(x = Baths) +
geom_bar() 
ggplot(data = data1) +
aes(x = Quality) +
geom_bar() 
ggplot(data = data1) +
aes(x = Garage) +
geom_bar() 
ggplot(data = data1) +
aes(x = Year) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Multikolinearnost
pairs.panels(data1[,c(1:12)],
method = "pearson", # correlation method
hist.col = "#00AFBB",
density = TRUE, # show density plots
ellipse = FALSE
)
Dijagnostički testovi
ggplot(data = realestate_aug, aes(x = .fitted, y = .resid)) +
geom_point() +
geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
xlab("Fitted values") +
ylab("Residuals")
p <- ggplot(realestate_aug, aes(sample =.resid))
p+ stat_qq_point(size = 2) +
stat_qq_line() +
xlab("Theoretical Quantiles") + ylab("Sample Quantiles")
ggplot(data = realestate_aug, aes(x = .resid)) +
geom_histogram(binwidth =20) +
xlab("Residuals")
gg_resleverage(realestate)## `geom_smooth()` using formula 'y ~ x'
gg_cooksd(realestate)
Predikcija za puni model
predict(realestate, newdata=data.frame(Beds=c(3), AirCond=c(3), Style=c(3), Year=c(1998), SqFeet=c(2), Baths=c(3), Garage=c(2), Highway=c(0), Lot=c(22), Quality=c(2), Pool=c(1)), interval="prediction")## fit lwr upr
## 1 275.464 144.1638 406.7643Predikcija za površinu, broj kupaonica i kvalitetu
predict(realestate2, newdata=data.frame(SqFeet=c(2.3), Baths=c(2), Quality=c(2)), interval="prediction")## fit lwr upr
## 1 291.8885 153.8461 429.9308Predikcija za broj kreveta, garažu i godinu izgradnje
predict(realestate3, newdata=data.frame(Beds=c(3), Garage=c(2), Year=c(1998)), interval="prediction")## fit lwr upr
## 1 335.662 139.1182 532.2058Nakon provođenja deskriptivne analize uočili smo logičke varijable Highway, AirCond i Pool. Kvantitativne varijable su SalesPrice, SqFeet, Beds, Baths, Garage, Year, Quality, Style i Lot, a kvalitativne varijable nisu uočene.
Napravili smo puni model sa svim varijablama, gdje predviđamo vrijednost varijable SalesPrice. Nakon toga na temelju analize multikolinearnosti odabrali smo varijable koje najviše utjeću na SalesPrice i prema njima napravili dva reducirana modela.
Pomoću grafa reziduala i Cook-ovog dijagrama smo proveli dijagnostičke testove i zaključili da je opservacija 96 potencijalno stršilo. Smatramo da je to uzrokovano varijablama godina izgradnje (Year) i veličina dvorišta (Lot).
Prvi reducirani model je sadržavao varijable SqFeet, Quality i Baths, a drugi Beds, Garage i Year.
Logistička regresija
Deskriptivna analiza
summary(data3)## ID iznosKredita spol obrazovanje
## Min. : 1 Min. : 10000 Min. :1.000 Min. :0.000
## 1st Qu.: 7501 1st Qu.: 50000 1st Qu.:1.000 1st Qu.:1.000
## Median :15000 Median : 140000 Median :2.000 Median :2.000
## Mean :15000 Mean : 167484 Mean :1.604 Mean :1.853
## 3rd Qu.:22500 3rd Qu.: 240000 3rd Qu.:2.000 3rd Qu.:2.000
## Max. :30000 Max. :1000000 Max. :2.000 Max. :6.000
## bracnoStanje dob placanje1 placanje2
## Min. :0.000 Min. :21.00 Min. :-2.0000 Min. :-2.0000
## 1st Qu.:1.000 1st Qu.:28.00 1st Qu.:-1.0000 1st Qu.:-1.0000
## Median :2.000 Median :34.00 Median : 0.0000 Median : 0.0000
## Mean :1.552 Mean :35.49 Mean :-0.0167 Mean :-0.1338
## 3rd Qu.:2.000 3rd Qu.:41.00 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. :3.000 Max. :79.00 Max. : 8.0000 Max. : 8.0000
## placanje3 placanje4 placanje5 placanje6
## Min. :-2.0000 Min. :-2.0000 Min. :-2.0000 Min. :-2.0000
## 1st Qu.:-1.0000 1st Qu.:-1.0000 1st Qu.:-1.0000 1st Qu.:-1.0000
## Median : 0.0000 Median : 0.0000 Median : 0.0000 Median : 0.0000
## Mean :-0.1662 Mean :-0.2207 Mean :-0.2662 Mean :-0.2911
## 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000 3rd Qu.: 0.0000
## Max. : 8.0000 Max. : 8.0000 Max. : 8.0000 Max. : 8.0000
## racuni1 racuni2 racuni3 racuni4
## Min. :-165580 Min. :-69777 Min. :-157264 Min. :-170000
## 1st Qu.: 3559 1st Qu.: 2985 1st Qu.: 2666 1st Qu.: 2327
## Median : 22382 Median : 21200 Median : 20089 Median : 19052
## Mean : 51223 Mean : 49179 Mean : 47013 Mean : 43263
## 3rd Qu.: 67091 3rd Qu.: 64006 3rd Qu.: 60165 3rd Qu.: 54506
## Max. : 964511 Max. :983931 Max. :1664089 Max. : 891586
## racuni5 racuni6 placeno1 placeno2
## Min. :-81334 Min. :-339603 Min. : 0 Min. : 0
## 1st Qu.: 1763 1st Qu.: 1256 1st Qu.: 1000 1st Qu.: 833
## Median : 18105 Median : 17071 Median : 2100 Median : 2009
## Mean : 40311 Mean : 38872 Mean : 5664 Mean : 5921
## 3rd Qu.: 50191 3rd Qu.: 49198 3rd Qu.: 5006 3rd Qu.: 5000
## Max. :927171 Max. : 961664 Max. :873552 Max. :1684259
## placeno3 placeno4 placeno5 placeno6
## Min. : 0 Min. : 0 Min. : 0.0 Min. : 0.0
## 1st Qu.: 390 1st Qu.: 296 1st Qu.: 252.5 1st Qu.: 117.8
## Median : 1800 Median : 1500 Median : 1500.0 Median : 1500.0
## Mean : 5226 Mean : 4826 Mean : 4799.4 Mean : 5215.5
## 3rd Qu.: 4505 3rd Qu.: 4013 3rd Qu.: 4031.5 3rd Qu.: 4000.0
## Max. :896040 Max. :621000 Max. :426529.0 Max. :528666.0
## kasnjenje
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.2212
## 3rd Qu.:0.0000
## Max. :1.0000ind3 <- sample(c(TRUE, FALSE), nrow(data3), replace=T, prob = c(0.8, 0.2))
train3 <- data3[ind3, ]
test3 <- data3[!ind3, ]
kreditne <- glm(kasnjenje ~., family = "binomial", data = train3)
kreditne2 <- glm(kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje + dob + placanje1 + placanje2 + placanje3 + placanje5 + racuni1 + racuni2 + racuni3 + placeno1 + placeno2 + placeno4 + placeno5, family = "binomial", data = train3)
summary(kreditne)##
## Call:
## glm(formula = kasnjenje ~ ., family = "binomial", data = train3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.1420 -0.7000 -0.5507 -0.2954 3.8378
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.762e-01 1.350e-01 -5.008 5.50e-07 ***
## ID -4.574e-07 1.954e-06 -0.234 0.814901
## iznosKredita -6.807e-07 1.746e-07 -3.898 9.69e-05 ***
## spol -1.304e-01 3.436e-02 -3.794 0.000148 ***
## obrazovanje -9.586e-02 2.348e-02 -4.082 4.46e-05 ***
## bracnoStanje -1.527e-01 3.541e-02 -4.312 1.61e-05 ***
## dob 7.801e-03 1.983e-03 3.935 8.34e-05 ***
## placanje1 5.728e-01 1.975e-02 29.008 < 2e-16 ***
## placanje2 9.034e-02 2.247e-02 4.020 5.81e-05 ***
## placanje3 7.283e-02 2.523e-02 2.887 0.003890 **
## placanje4 7.964e-03 2.799e-02 0.285 0.775969
## placanje5 4.119e-02 3.006e-02 1.370 0.170636
## placanje6 8.150e-03 2.472e-02 0.330 0.741657
## racuni1 -4.800e-06 1.240e-06 -3.871 0.000108 ***
## racuni2 4.242e-07 1.682e-06 0.252 0.800945
## racuni3 2.473e-06 1.460e-06 1.694 0.090296 .
## racuni4 3.096e-07 1.468e-06 0.211 0.832974
## racuni5 -7.079e-07 1.720e-06 -0.411 0.680717
## racuni6 1.144e-06 1.388e-06 0.824 0.409864
## placeno1 -1.126e-05 2.408e-06 -4.675 2.94e-06 ***
## placeno2 -1.015e-05 2.304e-06 -4.405 1.06e-05 ***
## placeno3 -1.470e-06 1.808e-06 -0.813 0.416095
## placeno4 -3.352e-06 1.952e-06 -1.717 0.085994 .
## placeno5 -3.203e-06 1.938e-06 -1.653 0.098254 .
## placeno6 -3.755e-06 1.540e-06 -2.438 0.014759 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 25224 on 23813 degrees of freedom
## Residual deviance: 22236 on 23789 degrees of freedom
## AIC: 22286
##
## Number of Fisher Scoring iterations: 6glance(kreditne)## # A tibble: 1 × 8
## null.deviance df.null logLik AIC BIC deviance df.residual nobs
## <dbl> <int> <dbl> <dbl> <dbl> <dbl> <int> <int>
## 1 25224. 23813 -11118. 22286. 22488. 22236. 23789 23814ggplot(data = data3) +
aes(x = iznosKredita) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
ggplot(data = data3) +
aes(x = spol) +
geom_bar()
ggplot(data = data3) +
aes(x = obrazovanje) +
geom_bar()
ggplot(data = data3) +
aes(x = dob) +
geom_histogram()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Predikcije
test3.predicted <- predict(kreditne, newdata = test3, type = "response")
kreditnatest05 = table(test3$kasnjenje, test3.predicted > 0.5) |> prop.table() |> round(3)
kreditnatest07 = table(test3$kasnjenje, test3.predicted > 0.7) |> prop.table() |> round(3)
table(test3$kasnjenje, test3.predicted > 0.5)##
## FALSE TRUE
## 0 4719 121
## 1 1005 341table(test3$kasnjenje, test3.predicted > 0.7)##
## FALSE TRUE
## 0 4815 25
## 1 1287 59StepAIC
stepkreditne <- stepAIC(kreditne, direction="both")## Start: AIC=22286.09
## kasnjenje ~ ID + iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje4 + placanje5 +
## placanje6 + racuni1 + racuni2 + racuni3 + racuni4 + racuni5 +
## racuni6 + placeno1 + placeno2 + placeno3 + placeno4 + placeno5 +
## placeno6
##
## Df Deviance AIC
## - racuni4 1 22236 22284
## - ID 1 22236 22284
## - racuni2 1 22236 22284
## - placanje4 1 22236 22284
## - placanje6 1 22236 22284
## - racuni5 1 22236 22284
## - placeno3 1 22237 22285
## - racuni6 1 22237 22285
## - placanje5 1 22238 22286
## <none> 22236 22286
## - racuni3 1 22239 22287
## - placeno5 1 22239 22287
## - placeno4 1 22239 22287
## - placeno6 1 22243 22291
## - placanje3 1 22244 22292
## - spol 1 22250 22298
## - dob 1 22252 22300
## - iznosKredita 1 22252 22300
## - placanje2 1 22252 22300
## - obrazovanje 1 22253 22301
## - racuni1 1 22253 22301
## - bracnoStanje 1 22255 22303
## - placeno2 1 22260 22308
## - placeno1 1 22264 22312
## - placanje1 1 23075 23123
##
## Step: AIC=22284.14
## kasnjenje ~ ID + iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje4 + placanje5 +
## placanje6 + racuni1 + racuni2 + racuni3 + racuni5 + racuni6 +
## placeno1 + placeno2 + placeno3 + placeno4 + placeno5 + placeno6
##
## Df Deviance AIC
## - ID 1 22236 22282
## - racuni2 1 22236 22282
## - placanje4 1 22236 22282
## - placanje6 1 22236 22282
## - racuni5 1 22236 22282
## - placeno3 1 22237 22283
## - racuni6 1 22237 22283
## - placanje5 1 22238 22284
## <none> 22236 22284
## - placeno5 1 22239 22285
## - racuni3 1 22240 22286
## + racuni4 1 22236 22286
## - placeno4 1 22240 22286
## - placeno6 1 22243 22289
## - placanje3 1 22244 22290
## - spol 1 22251 22297
## - dob 1 22252 22298
## - iznosKredita 1 22252 22298
## - placanje2 1 22252 22298
## - obrazovanje 1 22253 22299
## - racuni1 1 22253 22299
## - bracnoStanje 1 22255 22301
## - placeno2 1 22261 22307
## - placeno1 1 22264 22310
## - placanje1 1 23075 23121
##
## Step: AIC=22282.19
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje4 + placanje5 +
## placanje6 + racuni1 + racuni2 + racuni3 + racuni5 + racuni6 +
## placeno1 + placeno2 + placeno3 + placeno4 + placeno5 + placeno6
##
## Df Deviance AIC
## - racuni2 1 22236 22280
## - placanje4 1 22236 22280
## - placanje6 1 22236 22280
## - racuni5 1 22236 22280
## - placeno3 1 22237 22281
## - racuni6 1 22237 22281
## - placanje5 1 22238 22282
## <none> 22236 22282
## - placeno5 1 22239 22283
## - racuni3 1 22240 22284
## + ID 1 22236 22284
## + racuni4 1 22236 22284
## - placeno4 1 22240 22284
## - placeno6 1 22243 22287
## - placanje3 1 22245 22289
## - spol 1 22251 22295
## - dob 1 22252 22296
## - iznosKredita 1 22252 22296
## - placanje2 1 22252 22296
## - obrazovanje 1 22253 22297
## - racuni1 1 22253 22297
## - bracnoStanje 1 22255 22299
## - placeno2 1 22261 22305
## - placeno1 1 22265 22309
## - placanje1 1 23075 23119
##
## Step: AIC=22280.25
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje4 + placanje5 +
## placanje6 + racuni1 + racuni3 + racuni5 + racuni6 + placeno1 +
## placeno2 + placeno3 + placeno4 + placeno5 + placeno6
##
## Df Deviance AIC
## - placanje4 1 22236 22278
## - placanje6 1 22236 22278
## - racuni5 1 22236 22278
## - placeno3 1 22237 22279
## - racuni6 1 22237 22279
## - placanje5 1 22238 22280
## <none> 22236 22280
## - placeno5 1 22239 22281
## + racuni2 1 22236 22282
## + ID 1 22236 22282
## + racuni4 1 22236 22282
## - placeno4 1 22240 22282
## - racuni3 1 22242 22284
## - placeno6 1 22243 22285
## - placanje3 1 22245 22287
## - spol 1 22251 22293
## - dob 1 22252 22294
## - iznosKredita 1 22252 22294
## - placanje2 1 22252 22294
## - obrazovanje 1 22253 22295
## - bracnoStanje 1 22255 22297
## - placeno2 1 22266 22308
## - racuni1 1 22270 22312
## - placeno1 1 22271 22313
## - placanje1 1 23076 23118
##
## Step: AIC=22278.33
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje5 + placanje6 +
## racuni1 + racuni3 + racuni5 + racuni6 + placeno1 + placeno2 +
## placeno3 + placeno4 + placeno5 + placeno6
##
## Df Deviance AIC
## - placanje6 1 22236 22276
## - racuni5 1 22237 22277
## - racuni6 1 22237 22277
## - placeno3 1 22237 22277
## <none> 22236 22278
## - placeno5 1 22239 22279
## - placanje5 1 22239 22279
## + placanje4 1 22236 22280
## + racuni2 1 22236 22280
## + ID 1 22236 22280
## + racuni4 1 22236 22280
## - placeno4 1 22241 22281
## - racuni3 1 22243 22283
## - placeno6 1 22243 22283
## - placanje3 1 22248 22288
## - spol 1 22251 22291
## - dob 1 22252 22292
## - iznosKredita 1 22252 22292
## - placanje2 1 22252 22292
## - obrazovanje 1 22253 22293
## - bracnoStanje 1 22255 22295
## - placeno2 1 22266 22306
## - racuni1 1 22270 22310
## - placeno1 1 22271 22311
## - placanje1 1 23082 23122
##
## Step: AIC=22276.44
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje5 + racuni1 +
## racuni3 + racuni5 + racuni6 + placeno1 + placeno2 + placeno3 +
## placeno4 + placeno5 + placeno6
##
## Df Deviance AIC
## - racuni5 1 22237 22275
## - racuni6 1 22237 22275
## - placeno3 1 22237 22275
## <none> 22236 22276
## - placeno5 1 22240 22278
## + placanje6 1 22236 22278
## + placanje4 1 22236 22278
## + racuni2 1 22236 22278
## + ID 1 22236 22278
## + racuni4 1 22236 22278
## - placeno4 1 22241 22279
## - racuni3 1 22243 22281
## - placanje5 1 22243 22281
## - placeno6 1 22243 22281
## - placanje3 1 22248 22286
## - spol 1 22251 22289
## - dob 1 22252 22290
## - iznosKredita 1 22252 22290
## - placanje2 1 22253 22291
## - obrazovanje 1 22254 22292
## - bracnoStanje 1 22255 22293
## - placeno2 1 22266 22304
## - racuni1 1 22270 22308
## - placeno1 1 22271 22309
## - placanje1 1 23083 23121
##
## Step: AIC=22274.56
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje5 + racuni1 +
## racuni3 + racuni6 + placeno1 + placeno2 + placeno3 + placeno4 +
## placeno5 + placeno6
##
## Df Deviance AIC
## - placeno3 1 22238 22274
## - racuni6 1 22238 22274
## <none> 22237 22275
## - placeno5 1 22240 22276
## + racuni5 1 22236 22276
## + placanje6 1 22237 22277
## + placanje4 1 22237 22277
## + racuni2 1 22237 22277
## + ID 1 22237 22277
## + racuni4 1 22237 22277
## - placeno4 1 22242 22278
## - racuni3 1 22243 22279
## - placanje5 1 22243 22279
## - placeno6 1 22243 22279
## - placanje3 1 22248 22284
## - spol 1 22251 22287
## - dob 1 22252 22288
## - iznosKredita 1 22253 22289
## - placanje2 1 22253 22289
## - obrazovanje 1 22254 22290
## - bracnoStanje 1 22255 22291
## - placeno2 1 22266 22302
## - racuni1 1 22271 22307
## - placeno1 1 22271 22307
## - placanje1 1 23083 23119
##
## Step: AIC=22273.5
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje5 + racuni1 +
## racuni3 + racuni6 + placeno1 + placeno2 + placeno4 + placeno5 +
## placeno6
##
## Df Deviance AIC
## - racuni6 1 22238 22272
## <none> 22238 22274
## + placeno3 1 22237 22275
## - placeno5 1 22241 22275
## + racuni5 1 22237 22275
## + racuni4 1 22237 22275
## + placanje4 1 22237 22275
## + placanje6 1 22237 22275
## + ID 1 22237 22275
## + racuni2 1 22237 22275
## - placeno4 1 22243 22277
## - placanje5 1 22244 22278
## - placeno6 1 22245 22279
## - racuni3 1 22246 22280
## - placanje3 1 22249 22283
## - spol 1 22252 22286
## - dob 1 22253 22287
## - placanje2 1 22254 22288
## - iznosKredita 1 22254 22288
## - obrazovanje 1 22255 22289
## - bracnoStanje 1 22256 22290
## - placeno2 1 22270 22304
## - racuni1 1 22274 22308
## - placeno1 1 22275 22309
## - placanje1 1 23087 23121
##
## Step: AIC=22272.22
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje5 + racuni1 +
## racuni3 + placeno1 + placeno2 + placeno4 + placeno5 + placeno6
##
## Df Deviance AIC
## <none> 22238 22272
## - placeno5 1 22241 22273
## + racuni6 1 22238 22274
## + placeno3 1 22238 22274
## + placanje6 1 22238 22274
## + racuni5 1 22238 22274
## + placanje4 1 22238 22274
## + racuni2 1 22238 22274
## + ID 1 22238 22274
## + racuni4 1 22238 22274
## - placeno4 1 22243 22275
## - placanje5 1 22245 22277
## - placeno6 1 22246 22278
## - placanje3 1 22250 22282
## - spol 1 22252 22284
## - racuni3 1 22253 22285
## - dob 1 22254 22286
## - placanje2 1 22254 22286
## - iznosKredita 1 22254 22286
## - obrazovanje 1 22256 22288
## - bracnoStanje 1 22257 22289
## - placeno2 1 22273 22305
## - racuni1 1 22275 22307
## - placeno1 1 22276 22308
## - placanje1 1 23090 23122stepkreditne$anova## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## kasnjenje ~ ID + iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje4 + placanje5 +
## placanje6 + racuni1 + racuni2 + racuni3 + racuni4 + racuni5 +
## racuni6 + placeno1 + placeno2 + placeno3 + placeno4 + placeno5 +
## placeno6
##
## Final Model:
## kasnjenje ~ iznosKredita + spol + obrazovanje + bracnoStanje +
## dob + placanje1 + placanje2 + placanje3 + placanje5 + racuni1 +
## racuni3 + placeno1 + placeno2 + placeno4 + placeno5 + placeno6
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 23789 22236.09 22286.09
## 2 - racuni4 1 0.04434569 23790 22236.14 22284.14
## 3 - ID 1 0.04698887 23791 22236.19 22282.19
## 4 - racuni2 1 0.06902413 23792 22236.25 22280.25
## 5 - placanje4 1 0.07548744 23793 22236.33 22278.33
## 6 - placanje6 1 0.11093016 23794 22236.44 22276.44
## 7 - racuni5 1 0.12142213 23795 22236.56 22274.56
## 8 - placeno3 1 0.94000079 23796 22237.50 22273.50
## 9 - racuni6 1 0.71718400 23797 22238.22 22272.22Predikcije finalni model
test3.predicted <- predict(kreditne2, newdata = test3, type = "response")
kreditnatest05.2 = table(test3$kasnjenje, test3.predicted > 0.5) |> prop.table() |> round(3)
kreditnatest07.2 = table(test3$kasnjenje, test3.predicted > 0.7) |> prop.table() |> round(3)
table(test3$kasnjenje, test3.predicted > 0.5)##
## FALSE TRUE
## 0 4719 121
## 1 1010 336table(test3$kasnjenje, test3.predicted > 0.7)##
## FALSE TRUE
## 0 4816 24
## 1 1286 60Nakon izrade deskrpitivne analize smo došli do zaključka da je varijabla kasnjenje jedina logička varijabla, te nam je ta varijabla bitna za predikcije, s obzirom da istražujemo kreditne kartice. Po pitanju ostalih varijabli uočili smo da su spol, bracnoStanje i obrazovanje kvalitativne varijable. Sve ostale varijable su kvantitativne.
Točnost pre-stepAIC klasifikacije je bila 76.33% za p = 0.5, i 72.31% za p = 0.7. Zaključili smo da je klasifikacija točnija za vrijednost p = 0.5.
Funkcijom stepAIC došli smo do zaključka da finalani prediktvni model treba sadržavati varijable iznosKredita, spol, obrazovanje, bracnoStanje, dob, placanje1, placanje2, placanje3, placanje5, racuni1, racuni2, racuni6, placeno1, placeno2, placeno3, placeno4 i placeno5.
Točnost post-stepAIC klasifikacije je bila 76.2% za p = 0.5, i 72.25% za p = 0.7. Zaključili smo da je klasifikacija točnija za vrijednost p = 0.5.
Točnost post-stepAIC modela je vrlo bliska točnosti punog modela iako sadrži 7 varijabli manje.
Regresijsko stablo odlučivanja
set.seed(1234)
ind <- sample(2, nrow(data1), replace=T, prob = c(0.7, 0.3))
train <- data1[ind == 1,]
test <- data1[ind == 2,]
tree <- rpart(SalesPrice ~., data = train, method='anova')
rpart.plot(tree)
printcp(tree)##
## Regression tree:
## rpart(formula = SalesPrice ~ ., data = train, method = "anova")
##
## Variables actually used in tree construction:
## [1] Baths Lot Quality SqFeet Year
##
## Root node error: 6967815/363 = 19195
##
## n= 363
##
## CP nsplit rel error xerror xstd
## 1 0.555951 0 1.00000 1.01182 0.105439
## 2 0.153545 1 0.44405 0.45481 0.048247
## 3 0.045367 2 0.29050 0.35009 0.040930
## 4 0.030290 3 0.24514 0.26460 0.034845
## 5 0.025240 4 0.21485 0.26725 0.035304
## 6 0.011862 5 0.18961 0.24147 0.029276
## 7 0.010000 6 0.17775 0.24375 0.030209plotcp(tree)
Stablo koje smo vizualizirali ima 6 čvorova jer smo u printcp funckiji za vrijednost 6 dobili najmanju xerror vrijednost.
U multiploj regresiji smo izračunali predikciju vrijednost varijable SalesPrice i dobili rezultat 275.464, dok smo kroz regresijsko stablo odlučivanja dobili rezulat 244. Dobivena vrijednsot je bila približna.
Klasifikacijsko stablo odlučivanja
set.seed(1243)
summary(data2)## Area Perimeter MajorAxisLength MinorAxisLength
## Min. : 20420 Min. : 524.7 Min. :183.6 Min. :122.5
## 1st Qu.: 36328 1st Qu.: 703.5 1st Qu.:253.3 1st Qu.:175.8
## Median : 44652 Median : 794.9 Median :296.9 Median :192.4
## Mean : 53048 Mean : 855.3 Mean :320.1 Mean :202.3
## 3rd Qu.: 61332 3rd Qu.: 977.2 3rd Qu.:376.5 3rd Qu.:217.0
## Max. :254616 Max. :1985.4 Max. :738.9 Max. :460.2
##
## AspectRation Eccentricity ConvexArea EquivDiameter
## Min. :1.025 Min. :0.2190 Min. : 20684 Min. :161.2
## 1st Qu.:1.432 1st Qu.:0.7159 1st Qu.: 36715 1st Qu.:215.1
## Median :1.551 Median :0.7644 Median : 45178 Median :238.4
## Mean :1.583 Mean :0.7509 Mean : 53768 Mean :253.1
## 3rd Qu.:1.707 3rd Qu.:0.8105 3rd Qu.: 62294 3rd Qu.:279.4
## Max. :2.430 Max. :0.9114 Max. :263261 Max. :569.4
##
## Extent Solidity roundness Compactness
## Min. :0.5553 Min. :0.9192 Min. :0.4896 Min. :0.6406
## 1st Qu.:0.7186 1st Qu.:0.9857 1st Qu.:0.8321 1st Qu.:0.7625
## Median :0.7599 Median :0.9883 Median :0.8832 Median :0.8013
## Mean :0.7497 Mean :0.9871 Mean :0.8733 Mean :0.7999
## 3rd Qu.:0.7869 3rd Qu.:0.9900 3rd Qu.:0.9169 3rd Qu.:0.8343
## Max. :0.8662 Max. :0.9947 Max. :0.9907 Max. :0.9873
##
## ShapeFactor1 ShapeFactor2 ShapeFactor3 ShapeFactor4
## Min. :0.002778 Min. :0.0005642 Min. :0.4103 Min. :0.9477
## 1st Qu.:0.005900 1st Qu.:0.0011535 1st Qu.:0.5814 1st Qu.:0.9937
## Median :0.006645 Median :0.0016935 Median :0.6420 Median :0.9964
## Mean :0.006564 Mean :0.0017159 Mean :0.6436 Mean :0.9951
## 3rd Qu.:0.007271 3rd Qu.:0.0021703 3rd Qu.:0.6960 3rd Qu.:0.9979
## Max. :0.010451 Max. :0.0036650 Max. :0.9748 Max. :0.9997
##
## Class
## BARBUNYA:1322
## BOMBAY : 522
## CALI :1630
## DERMASON:3546
## HOROZ :1928
## SEKER :2027
## SIRA :2636ggplot(data = data2) +
aes(x = Class) +
geom_bar()
ind2 <- sample(c(TRUE, FALSE), nrow(data2), replace=T, prob = c(0.8, 0.2))
train2 <- data2[ind2, ]
test2 <- data2[!ind2, ]
tree2 <- rpart(Class~., data = train2, method='class')
rpart.plot(tree2, box.palette = as.list(rainbow(7)))
printcp(tree2)##
## Classification tree:
## rpart(formula = Class ~ ., data = train2, method = "class")
##
## Variables actually used in tree construction:
## [1] Compactness MajorAxisLength MinorAxisLength Perimeter
## [5] roundness ShapeFactor1
##
## Root node error: 7998/10834 = 0.73823
##
## n= 10834
##
## CP nsplit rel error xerror xstd
## 1 0.197049 0 1.00000 1.00000 0.0057209
## 2 0.171793 1 0.80295 0.80345 0.0063932
## 3 0.163166 2 0.63116 0.62041 0.0064840
## 4 0.146537 3 0.46799 0.47099 0.0061978
## 5 0.065141 4 0.32146 0.32471 0.0055558
## 6 0.018630 6 0.19117 0.19605 0.0045787
## 7 0.010628 7 0.17254 0.17767 0.0043932
## 8 0.010000 8 0.16192 0.17392 0.0043535plotcp(tree2)
predikcije <- predict(tree2, test2, type='class')
confusionMatrix(predikcije, test2$Class)## Confusion Matrix and Statistics
##
## Reference
## Prediction BARBUNYA BOMBAY CALI DERMASON HOROZ SEKER SIRA
## BARBUNYA 212 0 35 0 4 2 1
## BOMBAY 0 116 0 0 0 0 0
## CALI 19 0 281 0 13 0 3
## DERMASON 0 0 0 649 2 19 74
## HOROZ 3 0 19 0 340 0 0
## SEKER 1 0 0 9 0 364 6
## SIRA 5 0 2 52 18 45 483
##
## Overall Statistics
##
## Accuracy : 0.8804
## 95% CI : (0.8678, 0.8923)
## No Information Rate : 0.2557
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.855
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: BARBUNYA Class: BOMBAY Class: CALI Class: DERMASON
## Sensitivity 0.88333 1.00000 0.8338 0.9141
## Specificity 0.98345 1.00000 0.9857 0.9540
## Pos Pred Value 0.83465 1.00000 0.8892 0.8723
## Neg Pred Value 0.98890 1.00000 0.9772 0.9700
## Prevalence 0.08642 0.04177 0.1214 0.2557
## Detection Rate 0.07634 0.04177 0.1012 0.2337
## Detection Prevalence 0.09147 0.04177 0.1138 0.2679
## Balanced Accuracy 0.93339 1.00000 0.9097 0.9341
## Class: HOROZ Class: SEKER Class: SIRA
## Sensitivity 0.9019 0.8465 0.8519
## Specificity 0.9908 0.9932 0.9448
## Pos Pred Value 0.9392 0.9579 0.7983
## Neg Pred Value 0.9847 0.9725 0.9613
## Prevalence 0.1358 0.1548 0.2042
## Detection Rate 0.1224 0.1311 0.1739
## Detection Prevalence 0.1304 0.1368 0.2179
## Balanced Accuracy 0.9463 0.9198 0.8983options(warn = defaultW)Varijabla Class je jedina kvalitativna varijabla, a sve ostale varijable su kvantitativne.
Stablo koje smo vizualizirali ima 9 čvorova.
U konfuzijskoj matrici smo uočili da je klasa Bombay u potpunosti točno klasificirana, klasa Sira ima najveću pogrešku u klasifikaciji, čak 25.47% Sira grahova je krivo klasificirano.