diff --git a/.DS_Store b/.DS_Store index 4e5ac95..2e44645 100644 Binary files a/.DS_Store and b/.DS_Store differ diff --git a/R/.DS_Store b/R/.DS_Store new file mode 100644 index 0000000..c7a9639 Binary files /dev/null and b/R/.DS_Store differ diff --git a/R/Credit Rating/Credit.csv b/R/Credit Rating/Credit.csv new file mode 100755 index 0000000..9208862 --- /dev/null +++ b/R/Credit Rating/Credit.csv @@ -0,0 +1,401 @@ +,Income,Limit,Rating,Cards,Age,Education,Gender,Student,Married,Ethnicity,Balance +1,14.891,3606,283,2,34,11, Male,No,Yes,Caucasian,333 +2,106.025,6645,483,3,82,15,Female,Yes,Yes,Asian,903 +3,104.593,7075,514,4,71,11, Male,No,No,Asian,580 +4,148.924,9504,681,3,36,11,Female,No,No,Asian,964 +5,55.882,4897,357,2,68,16, Male,No,Yes,Caucasian,331 +6,80.18,8047,569,4,77,10, Male,No,No,Caucasian,1151 +7,20.996,3388,259,2,37,12,Female,No,No,African American,203 +8,71.408,7114,512,2,87,9, Male,No,No,Asian,872 +9,15.125,3300,266,5,66,13,Female,No,No,Caucasian,279 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Male,No,No,Caucasian,136 +272,44.978,4866,347,1,30,10,Female,No,No,Caucasian,436 +273,30.413,3690,299,2,25,15,Female,Yes,No,Asian,728 +274,16.751,4706,353,6,48,14, Male,Yes,No,Asian,1255 +275,30.55,5869,439,5,81,9,Female,No,No,African American,967 +276,163.329,8732,636,3,50,14, Male,No,Yes,Caucasian,529 +277,23.106,3476,257,2,50,15,Female,No,No,Caucasian,209 +278,41.532,5000,353,2,50,12, Male,No,Yes,Caucasian,531 +279,128.04,6982,518,2,78,11,Female,No,Yes,Caucasian,250 +280,54.319,3063,248,3,59,8,Female,Yes,No,Caucasian,269 +281,53.401,5319,377,3,35,12,Female,No,No,African American,541 +282,36.142,1852,183,3,33,13,Female,No,No,African American,0 +283,63.534,8100,581,2,50,17,Female,No,Yes,Caucasian,1298 +284,49.927,6396,485,3,75,17,Female,No,Yes,Caucasian,890 +285,14.711,2047,167,2,67,6, Male,No,Yes,Caucasian,0 +286,18.967,1626,156,2,41,11,Female,No,Yes,Asian,0 +287,18.036,1552,142,2,48,15,Female,No,No,Caucasian,0 +288,60.449,3098,272,4,69,8, Male,No,Yes,Caucasian,0 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+306,24.46,1924,165,2,50,14,Female,No,Yes,Asian,0 +307,45.12,3762,287,3,80,8, Male,No,Yes,Caucasian,70 +308,75.406,3874,298,3,41,14,Female,No,Yes,Asian,0 +309,14.956,4640,332,2,33,6, Male,No,No,Asian,681 +310,75.257,7010,494,3,34,18,Female,No,Yes,Caucasian,885 +311,33.694,4891,369,1,52,16, Male,Yes,No,African American,1036 +312,23.375,5429,396,3,57,15,Female,No,Yes,Caucasian,844 +313,27.825,5227,386,6,63,11, Male,No,Yes,Caucasian,823 +314,92.386,7685,534,2,75,18,Female,No,Yes,Asian,843 +315,115.52,9272,656,2,69,14, Male,No,No,African American,1140 +316,14.479,3907,296,3,43,16, Male,No,Yes,Caucasian,463 +317,52.179,7306,522,2,57,14, Male,No,No,Asian,1142 +318,68.462,4712,340,2,71,16, Male,No,Yes,Caucasian,136 +319,18.951,1485,129,3,82,13,Female,No,No,Caucasian,0 +320,27.59,2586,229,5,54,16, Male,No,Yes,African American,0 +321,16.279,1160,126,3,78,13, Male,Yes,Yes,African American,5 +322,25.078,3096,236,2,27,15,Female,No,Yes,Caucasian,81 +323,27.229,3484,282,6,51,11, Male,No,No,Caucasian,265 +324,182.728,13913,982,4,98,17, Male,No,Yes,Caucasian,1999 +325,31.029,2863,223,2,66,17, Male,Yes,Yes,Asian,415 +326,17.765,5072,364,1,66,12,Female,No,Yes,Caucasian,732 +327,125.48,10230,721,3,82,16, Male,No,Yes,Caucasian,1361 +328,49.166,6662,508,3,68,14,Female,No,No,Asian,984 +329,41.192,3673,297,3,54,16,Female,No,Yes,Caucasian,121 +330,94.193,7576,527,2,44,16,Female,No,Yes,Caucasian,846 +331,20.405,4543,329,2,72,17, Male,Yes,No,Asian,1054 +332,12.581,3976,291,2,48,16, Male,No,Yes,Caucasian,474 +333,62.328,5228,377,3,83,15, Male,No,No,Caucasian,380 +334,21.011,3402,261,2,68,17, Male,No,Yes,African American,182 +335,24.23,4756,351,2,64,15,Female,No,Yes,Caucasian,594 +336,24.314,3409,270,2,23,7,Female,No,Yes,Caucasian,194 +337,32.856,5884,438,4,68,13, Male,No,No,Caucasian,926 +338,12.414,855,119,3,32,12, Male,No,Yes,African American,0 +339,41.365,5303,377,1,45,14, Male,No,No,Caucasian,606 +340,149.316,10278,707,1,80,16, Male,No,No,African American,1107 +341,27.794,3807,301,4,35,8,Female,No,Yes,African American,320 +342,13.234,3922,299,2,77,17,Female,No,Yes,Caucasian,426 +343,14.595,2955,260,5,37,9, Male,No,Yes,African American,204 +344,10.735,3746,280,2,44,17,Female,No,Yes,Caucasian,410 +345,48.218,5199,401,7,39,10, Male,No,Yes,Asian,633 +346,30.012,1511,137,2,33,17, Male,No,Yes,Caucasian,0 +347,21.551,5380,420,5,51,18, Male,No,Yes,Asian,907 +348,160.231,10748,754,2,69,17, Male,No,No,Caucasian,1192 +349,13.433,1134,112,3,70,14, Male,No,Yes,Caucasian,0 +350,48.577,5145,389,3,71,13,Female,No,Yes,Asian,503 +351,30.002,1561,155,4,70,13,Female,No,Yes,Caucasian,0 +352,61.62,5140,374,1,71,9, Male,No,Yes,Caucasian,302 +353,104.483,7140,507,2,41,14, Male,No,Yes,African American,583 +354,41.868,4716,342,2,47,18, Male,No,No,Caucasian,425 +355,12.068,3873,292,1,44,18,Female,No,Yes,Asian,413 +356,180.682,11966,832,2,58,8,Female,No,Yes,African American,1405 +357,34.48,6090,442,3,36,14, Male,No,No,Caucasian,962 +358,39.609,2539,188,1,40,14, Male,No,Yes,Asian,0 +359,30.111,4336,339,1,81,18, Male,No,Yes,Caucasian,347 +360,12.335,4471,344,3,79,12, Male,No,Yes,African American,611 +361,53.566,5891,434,4,82,10,Female,No,No,Caucasian,712 +362,53.217,4943,362,2,46,16,Female,No,Yes,Asian,382 +363,26.162,5101,382,3,62,19,Female,No,No,African American,710 +364,64.173,6127,433,1,80,10, Male,No,Yes,Caucasian,578 +365,128.669,9824,685,3,67,16, Male,No,Yes,Asian,1243 +366,113.772,6442,489,4,69,15, Male,Yes,Yes,Caucasian,790 +367,61.069,7871,564,3,56,14, Male,No,Yes,Caucasian,1264 +368,23.793,3615,263,2,70,14, Male,No,No,African American,216 +369,89,5759,440,3,37,6,Female,No,No,Caucasian,345 +370,71.682,8028,599,3,57,16, Male,No,Yes,Caucasian,1208 +371,35.61,6135,466,4,40,12, Male,No,No,Caucasian,992 +372,39.116,2150,173,4,75,15, Male,No,No,Caucasian,0 +373,19.782,3782,293,2,46,16,Female,Yes,No,Caucasian,840 +374,55.412,5354,383,2,37,16,Female,Yes,Yes,Caucasian,1003 +375,29.4,4840,368,3,76,18,Female,No,Yes,Caucasian,588 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Male,No,No,Asian,0 +394,17.316,1335,138,2,65,13, Male,No,No,African American,0 +395,49.794,5758,410,4,40,8, Male,No,No,Caucasian,734 +396,12.096,4100,307,3,32,13, Male,No,Yes,Caucasian,560 +397,13.364,3838,296,5,65,17, Male,No,No,African American,480 +398,57.872,4171,321,5,67,12,Female,No,Yes,Caucasian,138 +399,37.728,2525,192,1,44,13, Male,No,Yes,Caucasian,0 +400,18.701,5524,415,5,64,7,Female,No,No,Asian,966 diff --git a/R/Credit Rating/credit_description.txt b/R/Credit Rating/credit_description.txt new file mode 100755 index 0000000..50b00a7 --- /dev/null +++ b/R/Credit Rating/credit_description.txt @@ -0,0 +1,15 @@ +"Credit.csv" data description + +Column Variable name Description +A " " Identifier +B Income Income in $000 +C Limit Credit limit in $ +D Rating Credit rating score given at the issue of the most recent credit card +E Cards Number of credit cards held +F Age Age of the individual in years +G Education Years of education +H Gender Gender - recorded as Male or Female +I Student Yes = student; No = non-student +J Married Yes = married; No = not married +K Ethnicity Recorded as Caucasian, Asian or African American +L Balance Balance of credit account in $ diff --git a/R/Credit Rating/week1_credit.R b/R/Credit Rating/week1_credit.R new file mode 100644 index 0000000..39dd7a7 --- /dev/null +++ b/R/Credit Rating/week1_credit.R @@ -0,0 +1,158 @@ +##################################################### +#Reading in the Credit data +##################################################### +data = read.csv("Credit.csv", header = TRUE, sep=",") + +##################################################### +#Model #1: All numerical variables + +##################################################### +fit1<-lm(Balance~Income+Limit+Rating+Cards+Age+Education,data=data) +#look at the summary of the linear model fit +summary(fit1) + +# creating a dummy variable for Gender +gender_dummy <- ifelse(data$Gender == 'Female', 1, 0) + +# creating a dummy variable for Married +married_dummy <- ifelse(data$Married == 'Yes', 1, 0) + +# creating a dummy variable for Student +student_dummy <- ifelse(data$Student == 'Yes', 1, 0) + +# adding the dummy variables to the dataframe +data[,13] = gender_dummy #V13 +data[,14] = married_dummy #V14 +data[,15] = student_dummy #V15 + +##################################################### +#Model #2: With dummy variables + +##################################################### +fit2<-lm(Balance~Income+Limit+Rating+Cards+Age+Education+V13+V14+V15,data=data) +#look at the summary of the linear model fit +summary(fit2) + +# creating a dummy variable for Asian Ethinicity +asian_dummy <- ifelse(data$Ethnicity == 'Asian', 1, 0) + +# creating a dummy variable for African Ethinicity +african_dummy <- ifelse(data$Ethnicity == 'African American', 1, 0) + +data[,16] = asian_dummy #V16 +data[,17] = african_dummy #V17 + +##################################################### +#Model #3: With dummy variables (ethinicity) + +##################################################### +fit3<-lm(Balance~Income+Limit+Rating+Cards+Age+Education+V13+V14+V15+V16+V17,data=data) +#look at the summary of the linear model fit +summary(fit3) + +#plot scatter of residuals vs Income +plot(fit3$residuals~Income,data=data) +abline(h=0) + +#plot scatter of residuals vs Limit +plot(fit3$residuals~Limit,data=data) +abline(h=0) + +#plot scatter of residuals vs Rating +plot(fit3$residuals~Rating,data=data) +abline(h=0) + +#plot scatter of residuals vs Cards +plot(fit3$residuals~Cards,data=data) +abline(h=0) + +#plot scatter of residuals vs V15 +plot(fit3$residuals~V15,data=data) +abline(h=0) + +#plot scatter of residuals vs Age +plot(fit3$residuals~Age,data=data) +abline(h=0) + +##################################################### +#Defining a function for the wald test - require MASS library +#H0: RB=c vs Ha: RB!=c +#R=the R matrix +#B=the estimated coefficients +#S=the covariance matrix of B +#c=the vector of constants +##################################################### +library(MASS) +wald<-function(R,B,S,c){ + stats<-matrix(0,1,2) + dif=(R%*%B-c) + VV=R%*%(S)%*%t(R) + W=t(dif)%*%ginv(VV)%*%dif + stats[1]=W + stats[2]=pchisq(W,nrow(c),lower.tail=FALSE) + colnames(stats)<-c("Wald stat","p-value") + return(stats) +} + +#define inputs to the wald test - joint significance of the three slope parameters +RR=cbind(rbind(0,0,0,0,0,0,0,0,0,0,0),diag(11)) +cc=rbind(0,0,0,0,0,0,0,0,0,0,0) +bhat=(fit3$coefficients) +Shat=vcov(fit3) +wald1=wald(RR,bhat,Shat,cc) +wald1 + +########################################################### +#constructing quadratic terms for age, cards, limit +########################################################### +data[,18]=data$Age^2 +names(data)[names(data)=="V18"] <- "age2" + +data[,19]=data$Cards^2 +names(data)[names(data)=="V19"] <- "cards2" + +data[,20]=data$Limit^2 +names(data)[names(data)=="V20"] <- "limit2" + +##################################################### +#Model #4: Updated with transformations and multicolineariy + +##################################################### +fit4<-lm(Balance~Income+Limit+Cards+Age+Education+V13+V14+V15+age2+cards2+limit2,data=data) +#look at the summary of the linear model fit +summary(fit4) + + +##################################################### +#Analysis : Factors affecting credit balance + # Income | Limit | Cards | Age | Student | Limit^2 +##################################################### +#Modelling interactions - context! + +##################################################### +data[,21]=data$Limit*data$Cards +names(data)[names(data)=="V21"] <- "LimitxCards" +data[,22]=data$limit2*data$Cards +names(data)[names(data)=="V22"] <- "Limit2xCards" + +# Step 1 +fit_step1<-lm(Balance~Income+Limit+Cards+Age+V15+limit2+LimitxCards+Limit2xCards,data=data) +#look at the summary of the linear model fit +summary(fit_step1) + +# Step 2 +fit_step2<-lm(Balance~Income+Limit+Age+V15+limit2+LimitxCards+Limit2xCards,data=data) +#look at the summary of the linear model fit +summary(fit_step2) + +# Step 3 +fit_step3<-lm(Balance~Income+Limit+Age+V15+limit2+LimitxCards,data=data) +#look at the summary of the linear model fit +summary(fit_step3) + +# Step 4 +fit_step4<-lm(Balance~Income+Limit+V15+limit2+LimitxCards,data=data) +#look at the summary of the linear model fit +summary(fit_step4) + +step(fit_step4)