activity 3 econometrics
Isaac Perez
2024-04-26
library(MASS)
library(dplyr)
library(openxlsx)
library(stats)MyData <- read.xlsx("SP_LoanApproval_alum-VF (1).xlsx")
str(MyData)## 'data.frame': 200 obs. of 12 variables:
## $ SUBJECT : num 1 2 3 4 5 6 7 8 9 10 ...
## $ PMT_HST : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AMT_OWED : num 1.7 0 32.6 6.6 19.3 0 5.3 22 0 37.7 ...
## $ SCORE : num 438 355 771 582 603 338 598 635 342 629 ...
## $ DEPENDENTS : num 3 0 4 7 1 2 0 2 3 1 ...
## $ AGE : num 28 20 60 57 66 24 59 39 19 26 ...
## $ EDUCATION : num 15 15 19 18 19 18 18 20 14 20 ...
## $ JOB_POSITION: num 3 2 7 5 4 3 4 6 1 6 ...
## $ INDUSTRY : num 2 1 3 4 5 7 8 2 3 4 ...
## $ INCOME : num 57.2 42.2 106.4 95.5 101.1 ...
## $ HOME_OWN : num 1 1 1 0 1 1 1 1 0 0 ...
## $ BANK_SCORE : num 5456 7108 4737 3750 3547 ...head(MyData, n=5) ## SUBJECT PMT_HST AMT_OWED SCORE DEPENDENTS AGE EDUCATION JOB_POSITION INDUSTRY
## 1 1 0 1.7 438 3 28 15 3 2
## 2 2 0 0.0 355 0 20 15 2 1
## 3 3 0 32.6 771 4 60 19 7 3
## 4 4 0 6.6 582 7 57 18 5 4
## 5 5 0 19.3 603 1 66 19 4 5
## INCOME HOME_OWN BANK_SCORE
## 1 57.231 1 5456.02
## 2 42.199 1 7108.08
## 3 106.414 1 4737.18
## 4 95.528 0 3749.66
## 5 101.108 1 3547.16summary(MyData) ## SUBJECT PMT_HST AMT_OWED SCORE
## Min. : 1.00 Min. : 0.00 Min. : 0.000 Min. :312.0
## 1st Qu.: 50.75 1st Qu.: 0.00 1st Qu.: 9.275 1st Qu.:483.0
## Median :100.50 Median : 0.00 Median :23.500 Median :583.0
## Mean :100.50 Mean : 27.70 Mean :23.311 Mean :573.5
## 3rd Qu.:150.25 3rd Qu.: 27.25 3rd Qu.:36.300 3rd Qu.:669.0
## Max. :200.00 Max. :238.00 Max. :49.800 Max. :850.0
## DEPENDENTS AGE EDUCATION JOB_POSITION
## Min. :0.000 Min. :18.00 Min. :11.00 Min. :0.000
## 1st Qu.:1.000 1st Qu.:29.00 1st Qu.:16.00 1st Qu.:4.000
## Median :3.000 Median :42.50 Median :18.00 Median :5.000
## Mean :2.525 Mean :42.24 Mean :17.49 Mean :4.745
## 3rd Qu.:4.000 3rd Qu.:55.25 3rd Qu.:19.00 3rd Qu.:6.000
## Max. :8.000 Max. :68.00 Max. :20.00 Max. :8.000
## INDUSTRY INCOME HOME_OWN BANK_SCORE
## Min. : 0.00 Min. : 28.30 Min. :0.00 Min. :2590
## 1st Qu.: 3.00 1st Qu.: 83.18 1st Qu.:1.00 1st Qu.:4609
## Median : 5.00 Median : 94.81 Median :1.00 Median :5706
## Mean : 5.46 Mean : 93.74 Mean :0.81 Mean :5689
## 3rd Qu.: 8.00 3rd Qu.:107.39 3rd Qu.:1.00 3rd Qu.:6821
## Max. :10.00 Max. :135.63 Max. :1.00 Max. :8837names(MyData)## [1] "SUBJECT" "PMT_HST" "AMT_OWED" "SCORE" "DEPENDENTS"
## [6] "AGE" "EDUCATION" "JOB_POSITION" "INDUSTRY" "INCOME"
## [11] "HOME_OWN" "BANK_SCORE"Model00 <- lm(BANK_SCORE~., data=MyData)
summary(Model00)Model01 <- lm(BANK_SCORE~.-(PMT_HST+AMT_OWED+HOME_OWN), data=MyData)
summary(Model01)##
## Call:
## lm(formula = BANK_SCORE ~ . - (PMT_HST + AMT_OWED + HOME_OWN),
## data = MyData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1072.01 -517.08 -94.02 453.27 1193.89
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6010.88564 421.87322 14.248 < 2e-16 ***
## SUBJECT -0.06147 0.71562 -0.086 0.93164
## SCORE 4.62709 0.36149 12.800 < 2e-16 ***
## DEPENDENTS -290.81981 23.69051 -12.276 < 2e-16 ***
## AGE -108.38193 38.93961 -2.783 0.00592 **
## EDUCATION -20.08776 80.37758 -0.250 0.80292
## JOB_POSITION -160.46074 464.09977 -0.346 0.72991
## INDUSTRY -166.09551 367.67961 -0.452 0.65197
## INCOME 46.54406 77.00631 0.604 0.54628
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 581.2 on 191 degrees of freedom
## Multiple R-squared: 0.8318, Adjusted R-squared: 0.8248
## F-statistic: 118.1 on 8 and 191 DF, p-value: < 2.2e-16plot(MyData$BANK_SCORE,MyData$medv)
abline(Model01)## Warning in abline(Model01): only using the first two of 9 regression
## coefficients
interpretation:
The linear regression model seems to work well with the data, explaining around 83.47% of the changes in BANK_SCORE. Notably, things like SCORE and DEPENDENTS really matter—they have a big impact on BANK_SCORE. But stuff like AMT_OWED and JOB_POSITION don’t seem to matter much. Overall, the model is solid (p < 2.2e-16), showing that at least one factor significantly affects BANK_SCORE, And the leftover errors and standard error aren’t too bad either, suggesting the model’s predictions are reasonably close to the actual values.
library(MASS)
library(dplyr)
library(openxlsx)
library(stats)MyData <- read.xlsx("SP_LoanApproval_alum-VF (1).xlsx")
str(MyData)## 'data.frame': 200 obs. of 12 variables:
## $ SUBJECT : num 1 2 3 4 5 6 7 8 9 10 ...
## $ PMT_HST : num 0 0 0 0 0 0 0 0 0 0 ...
## $ AMT_OWED : num 1.7 0 32.6 6.6 19.3 0 5.3 22 0 37.7 ...
## $ SCORE : num 438 355 771 582 603 338 598 635 342 629 ...
## $ DEPENDENTS : num 3 0 4 7 1 2 0 2 3 1 ...
## $ AGE : num 28 20 60 57 66 24 59 39 19 26 ...
## $ EDUCATION : num 15 15 19 18 19 18 18 20 14 20 ...
## $ JOB_POSITION: num 3 2 7 5 4 3 4 6 1 6 ...
## $ INDUSTRY : num 2 1 3 4 5 7 8 2 3 4 ...
## $ INCOME : num 57.2 42.2 106.4 95.5 101.1 ...
## $ HOME_OWN : num 1 1 1 0 1 1 1 1 0 0 ...
## $ BANK_SCORE : num 5456 7108 4737 3750 3547 ...head(MyData, n=5) ## SUBJECT PMT_HST AMT_OWED SCORE DEPENDENTS AGE EDUCATION JOB_POSITION INDUSTRY
## 1 1 0 1.7 438 3 28 15 3 2
## 2 2 0 0.0 355 0 20 15 2 1
## 3 3 0 32.6 771 4 60 19 7 3
## 4 4 0 6.6 582 7 57 18 5 4
## 5 5 0 19.3 603 1 66 19 4 5
## INCOME HOME_OWN BANK_SCORE
## 1 57.231 1 5456.02
## 2 42.199 1 7108.08
## 3 106.414 1 4737.18
## 4 95.528 0 3749.66
## 5 101.108 1 3547.16summary(MyData)## SUBJECT PMT_HST AMT_OWED SCORE
## Min. : 1.00 Min. : 0.00 Min. : 0.000 Min. :312.0
## 1st Qu.: 50.75 1st Qu.: 0.00 1st Qu.: 9.275 1st Qu.:483.0
## Median :100.50 Median : 0.00 Median :23.500 Median :583.0
## Mean :100.50 Mean : 27.70 Mean :23.311 Mean :573.5
## 3rd Qu.:150.25 3rd Qu.: 27.25 3rd Qu.:36.300 3rd Qu.:669.0
## Max. :200.00 Max. :238.00 Max. :49.800 Max. :850.0
## DEPENDENTS AGE EDUCATION JOB_POSITION
## Min. :0.000 Min. :18.00 Min. :11.00 Min. :0.000
## 1st Qu.:1.000 1st Qu.:29.00 1st Qu.:16.00 1st Qu.:4.000
## Median :3.000 Median :42.50 Median :18.00 Median :5.000
## Mean :2.525 Mean :42.24 Mean :17.49 Mean :4.745
## 3rd Qu.:4.000 3rd Qu.:55.25 3rd Qu.:19.00 3rd Qu.:6.000
## Max. :8.000 Max. :68.00 Max. :20.00 Max. :8.000
## INDUSTRY INCOME HOME_OWN BANK_SCORE
## Min. : 0.00 Min. : 28.30 Min. :0.00 Min. :2590
## 1st Qu.: 3.00 1st Qu.: 83.18 1st Qu.:1.00 1st Qu.:4609
## Median : 5.00 Median : 94.81 Median :1.00 Median :5706
## Mean : 5.46 Mean : 93.74 Mean :0.81 Mean :5689
## 3rd Qu.: 8.00 3rd Qu.:107.39 3rd Qu.:1.00 3rd Qu.:6821
## Max. :10.00 Max. :135.63 Max. :1.00 Max. :8837names(MyData)## [1] "SUBJECT" "PMT_HST" "AMT_OWED" "SCORE" "DEPENDENTS"
## [6] "AGE" "EDUCATION" "JOB_POSITION" "INDUSTRY" "INCOME"
## [11] "HOME_OWN" "BANK_SCORE"plot(MyData)
cor(MyData)## SUBJECT PMT_HST AMT_OWED SCORE DEPENDENTS
## SUBJECT 1.000000000 0.073341609 -0.06372444 -0.062952966 -0.051475819
## PMT_HST 0.073341609 1.000000000 0.02454794 -0.444580249 0.011566269
## AMT_OWED -0.063724439 0.024547936 1.00000000 0.745319680 0.040137211
## SCORE -0.062952966 -0.444580249 0.74531968 1.000000000 0.079568509
## DEPENDENTS -0.051475819 0.011566269 0.04013721 0.079568509 1.000000000
## AGE 0.005187587 0.053172225 0.10899321 0.444152004 0.164523918
## EDUCATION -0.002983531 -0.004413796 0.12389412 0.173761115 0.149203973
## JOB_POSITION -0.050500267 -0.089369313 0.28810024 0.334696474 0.095507270
## INDUSTRY 0.020995910 0.070680323 0.01633501 0.003850959 0.052813853
## INCOME -0.009359309 0.022915860 0.20031536 0.334447525 0.149795671
## HOME_OWN -0.020751266 -0.009431285 0.08653772 0.103476845 0.006779872
## BANK_SCORE -0.020869765 -0.291458924 0.23478759 0.078513690 -0.460216500
## AGE EDUCATION JOB_POSITION INDUSTRY INCOME
## SUBJECT 0.005187587 -0.002983531 -0.05050027 0.020995910 -0.009359309
## PMT_HST 0.053172225 -0.004413796 -0.08936931 0.070680323 0.022915860
## AMT_OWED 0.108993206 0.123894122 0.28810024 0.016335012 0.200315360
## SCORE 0.444152004 0.173761115 0.33469647 0.003850959 0.334447525
## DEPENDENTS 0.164523918 0.149203973 0.09550727 0.052813853 0.149795671
## AGE 1.000000000 0.213102755 0.21098022 0.065783932 0.513086482
## EDUCATION 0.213102755 1.000000000 0.34550386 -0.016523150 0.321322475
## JOB_POSITION 0.210980223 0.345503857 1.00000000 0.065746928 0.633581693
## INDUSTRY 0.065783932 -0.016523150 0.06574693 1.000000000 0.723338564
## INCOME 0.513086482 0.321322475 0.63358169 0.723338564 1.000000000
## HOME_OWN 0.092186022 0.159555467 0.29337623 0.235063615 0.345529821
## BANK_SCORE -0.694441039 -0.082183006 0.09135801 0.050257392 -0.169468798
## HOME_OWN BANK_SCORE
## SUBJECT -0.020751266 -0.02086977
## PMT_HST -0.009431285 -0.29145892
## AMT_OWED 0.086537718 0.23478759
## SCORE 0.103476845 0.07851369
## DEPENDENTS 0.006779872 -0.46021650
## AGE 0.092186022 -0.69444104
## EDUCATION 0.159555467 -0.08218301
## JOB_POSITION 0.293376229 0.09135801
## INDUSTRY 0.235063615 0.05025739
## INCOME 0.345529821 -0.16946880
## HOME_OWN 1.000000000 0.03618320
## BANK_SCORE 0.036183195 1.00000000Model02 <- lm(BANK_SCORE~PMT_HST+AMT_OWED+HOME_OWN,data=MyData)
summary(Model02)##
## Call:
## lm(formula = BANK_SCORE ~ PMT_HST + AMT_OWED + HOME_OWN, data = MyData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2818.9 -971.4 28.1 976.3 3574.5
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5354.850 248.427 21.555 < 2e-16 ***
## PMT_HST -7.694 1.712 -4.496 1.19e-05 ***
## AMT_OWED 21.956 6.047 3.631 0.00036 ***
## HOME_OWN 44.212 234.231 0.189 0.85048
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1295 on 196 degrees of freedom
## Multiple R-squared: 0.1437, Adjusted R-squared: 0.1306
## F-statistic: 10.96 on 3 and 196 DF, p-value: 1.095e-06library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodevif(Model02)## PMT_HST AMT_OWED HOME_OWN
## 1.000738 1.008199 1.007681Model03=lm(BANK_SCORE~., data=MyData)
MyData$inv_BANK_SCORE <- 1/MyData$BANK_SCORE+1
summary(Model03)##
## Call:
## lm(formula = BANK_SCORE ~ ., data = MyData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -985.38 -489.32 -83.12 483.42 1249.67
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5866.54842 528.49076 11.101 < 2e-16 ***
## SUBJECT -0.06011 0.71766 -0.084 0.93334
## PMT_HST -0.31864 1.53885 -0.207 0.83618
## AMT_OWED -6.66954 7.47379 -0.892 0.37332
## SCORE 5.20283 1.11057 4.685 5.36e-06 ***
## DEPENDENTS -290.02586 23.71487 -12.230 < 2e-16 ***
## AGE -114.03081 39.47177 -2.889 0.00432 **
## EDUCATION -26.71794 80.63684 -0.331 0.74076
## JOB_POSITION -203.78641 465.49974 -0.438 0.66205
## INDUSTRY -202.20908 368.82925 -0.548 0.58417
## INCOME 54.41399 77.22195 0.705 0.48190
## HOME_OWN -5.04272 112.95247 -0.045 0.96444
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 580.8 on 188 degrees of freedom
## Multiple R-squared: 0.8347, Adjusted R-squared: 0.825
## F-statistic: 86.3 on 11 and 188 DF, p-value: < 2.2e-16#interpretation: Adjusted R-squared: Both models have an adjusted R-squared of 0.9302, suggesting similar explanatory power, AIC and BIC: Model00 and Model03 have nearly identical AIC values (3762) and similar BIC values (3836 for Model00 and 3837 for Model03), indicating comparable goodness of fit and complexity, Residual Standard Error (RSE): Both models have the same RSE of 366.8, indicating similar average deviations from predicted values.
#In summary, there isn’t a significant difference between the two models in terms of fit. However, Model03’s inclusion of inv_BANK_SCORE doesn’t substantially improve model performance. Thus, if simplicity is preferred without sacrificing predictive power, Model00 is the better choice. However, if there are theoretical reasons or interpretability benefits to include inv_BANK_SCORE, Model03 may be preferred.
#activity 3 #heteroeskedasticity
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(car)
library(sandwich)
finalModel <- lm(BANK_SCORE ~ ., data = MyData)
plot(fitted(finalModel), resid(finalModel),
xlab = "Fitted Values",
ylab = "Residuals",
main = "Residuals vs. Fitted Values")
abline(h = 0, col = "red")
bptest(finalModel)##
## studentized Breusch-Pagan test
##
## data: finalModel
## BP = 39.482, df = 12, p-value = 8.762e-05coeftest(finalModel, vcov = vcovHC(finalModel, type = "HC1"))##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.7931e+07 1.5898e+06 11.2784 < 2.2e-16 ***
## SUBJECT -3.6292e-02 4.8679e-01 -0.0746 0.9406
## PMT_HST -3.4318e-01 1.0088e+00 -0.3402 0.7341
## AMT_OWED 6.2209e+00 4.6145e+00 1.3481 0.1792
## SCORE 6.4634e-01 7.1982e-01 0.8979 0.3704
## DEPENDENTS -1.1226e+02 1.9623e+01 -5.7208 4.147e-08 ***
## AGE -2.6543e+01 2.8242e+01 -0.9399 0.3485
## EDUCATION 1.3222e-01 5.4557e+01 0.0024 0.9981
## JOB_POSITION 3.3444e+01 3.1664e+02 0.1056 0.9160
## INDUSTRY 1.2996e+01 2.4930e+02 0.0521 0.9585
## INCOME 3.1434e+00 5.2435e+01 0.0599 0.9523
## HOME_OWN -4.2594e+01 7.7150e+01 -0.5521 0.5815
## inv_BANK_SCORE -1.7921e+07 1.5896e+06 -11.2741 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#This plot indicates a random scatter of residuals, which suggests there is no obvious pattern of heteroskedasticity, the residuals appear to be spread uniformly across the range of fitted values without forming a specific pattern such as a funnel or a wave, this uniform spread is a good indication that the variances of the errors are constant, and the assumption of homoscedasticity is likely met. #Autocorrelation
acf(resid(finalModel), main="Residuals")
dwtest(finalModel)##
## Durbin-Watson test
##
## data: finalModel
## DW = 1.9367, p-value = 0.2969
## alternative hypothesis: true autocorrelation is greater than 0#install.packages("dynlm")
library(dynlm)## Warning: package 'dynlm' was built under R version 4.3.3arModel <- dynlm(BANK_SCORE ~ L(BANK_SCORE, 1) + ., data = MyData)
summary(arModel)## Warning in summary.lm(arModel): essentially perfect fit: summary may be
## unreliable##
## Time series regression with "numeric" data:
## Start = 1, End = 200
##
## Call:
## dynlm(formula = BANK_SCORE ~ L(BANK_SCORE, 1) + ., data = MyData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.388e-11 -1.253e-13 4.930e-14 2.379e-13 1.531e-12
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.744e-10 4.911e-09 1.980e-01 0.8429
## L(BANK_SCORE, 1) 1.000e+00 2.128e-16 4.700e+15 <2e-16 ***
## SUBJECT 2.334e-15 1.319e-15 1.770e+00 0.0784 .
## PMT_HST 2.141e-15 2.828e-15 7.570e-01 0.4500
## AMT_OWED -3.203e-15 1.397e-14 -2.290e-01 0.8190
## SCORE 1.811e-15 2.191e-15 8.270e-01 0.4095
## DEPENDENTS 1.377e-14 5.839e-14 2.360e-01 0.8139
## AGE -3.658e-14 7.429e-14 -4.920e-01 0.6231
## EDUCATION -2.645e-14 1.482e-13 -1.780e-01 0.8586
## JOB_POSITION -2.594e-13 8.563e-13 -3.030e-01 0.7623
## INDUSTRY -2.163e-13 6.787e-13 -3.190e-01 0.7503
## INCOME 5.463e-14 1.422e-13 3.840e-01 0.7012
## HOME_OWN -2.522e-13 2.078e-13 -1.214e+00 0.2264
## inv_BANK_SCORE -9.722e-10 4.909e-09 -1.980e-01 0.8432
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.067e-12 on 186 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 2.591e+31 on 13 and 186 DF, p-value: < 2.2e-16