Assigment 5 - ML
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Jan 9, 2024
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The following objects are masked from ‘package:ISLR’:
Auto, Credit
> library(MASS)
> library(car)
Error in library(car) : there is no package called ‘car’
> library(boot)
> library(class)
> # import data and clean
> capstr <- na.omit(capstr)
> dim(capstr)
[1] 5634 14
> names(capstr)
[1] "gvkey" "year" "conm" [4] "spquality" "industry" "leverage" [7] "logassets" "rdta" "cashta" [10] "divta" "taxes" "capexta" [13] "roa" "leverageincrease"
> #inspect your data
> mean(capstr$leverage)
[1] 0.3427896
> median(capstr$leverage)
[1] 0.3278918
> sd(capstr$leverage)
[1] 0.2064969
> #histograms of variables of interest
> hist(capstr$leverage)
> hist(capstr$logassets)
> #linear regression of leverage
> lm.fit1 <- lm(leverage~logassets, data=capstr)
> summary(lm.fit1)
Call:
lm(formula = leverage ~ logassets, data = capstr)
Residuals:
Min 1Q Median 3Q Max -0.36522 -0.14258 -0.01556 0.11545 1.50374 Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.250999 0.019425 12.922 < 2e-16 ***
logassets 0.010638 0.002228 4.773 1.86e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2061 on 5632 degrees of freedom
Multiple R-squared: 0.004029,
Adjusted R-squared: 0.003853 F-statistic: 22.79 on 1 and 5632 DF, p-value: 1.857e-06
> plot(lm.fit1)
Hit <Return> to see next plot: #training test split
Hit <Return> to see next plot: train<-(capstr$year<2018)
Hit <Return> to see next plot: test <- capstr[!train,]
Hit <Return> to see next plot: lm.fit3 <- lm(leverage~logassets, data=capstr, subset=train)
> mean((test$leverage-predict(lm.fit3, test))^2)
[1] 0.06209251
> #multiple regression
> lm.fit5 <- lm(leverage~logassets+capexta+rdta+taxes+spquality+divta+cashta, data=capstr, subset=train)
> summary(lm.fit5)
Call:
lm(formula = leverage ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, data = capstr, subset = train)
Residuals:
Min 1Q Median 3Q Max -0.49552 -0.11788 -0.01290 0.09373 1.30077 Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.215996 0.034405 6.278 4.08e-10 ***
logassets 0.009444 0.003231 2.923 0.003496 ** capexta -0.478974 0.130314 -3.676 0.000243 ***
rdta -0.872677 0.097419 -8.958 < 2e-16 ***
taxes -1.175891 0.591416 -1.988 0.046900 * spqualityA- 0.046032 0.021141 2.177 0.029550 * spqualityA+ -0.004828 0.028730 -0.168 0.866567 spqualityB 0.095494 0.018510 5.159 2.69e-07 ***
spqualityB- 0.093547 0.018623 5.023 5.47e-07 ***
spqualityB+ 0.110354 0.018303 6.029 1.91e-09 ***
spqualityC 0.194454 0.019839 9.801 < 2e-16 ***
spqualityD 0.384456 0.037757 10.182 < 2e-16 ***
divta 0.880130 0.171596 5.129 3.15e-07 ***
cashta -0.268161 0.034545 -7.763 1.24e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1842 on 2324 degrees of freedom
(4662 observations deleted due to missingness)
Multiple R-squared: 0.1952,
Adjusted R-squared: 0.1907 F-statistic: 43.35 on 13 and 2324 DF, p-value: < 2.2e-16
> mean((test$leverage-predict(lm.fit5, test))^2)
Error in eval(predvars, data, env) : object 'capexta' not found
> vif(lm.fit5)
Error in vif(lm.fit5) : could not find function "vif"
> #Add year and industry effects
> lm.fit6 <- lm(leverage~logassets+capexta+rdta+taxes+spquality+divta+cashta+factor(industry),
data=capstr,subset=train)
> summary(lm.fit6)
Call:
lm(formula = leverage ~ logassets + capexta + rdta + taxes + spquality + divta + cashta + factor(industry), data = capstr, subset = train)
Residuals:
Min 1Q Median 3Q Max -0.44866 -0.11462 -0.01504 0.09621 1.33151 Coefficients:
Estimate Std. Error t value
(Intercept) 0.2845002 0.0393679 7.227
logassets 0.0088708 0.0032623 2.719
capexta -0.2056597 0.1439220 -1.429
rdta -0.6576442 0.1036640 -6.344
taxes -0.4173570 0.5933910 -0.703
spqualityA- 0.0365232 0.0208753 1.750
spqualityA+ -0.0006213 0.0282817 -0.022
spqualityB 0.0792077 0.0184534 4.292
spqualityB- 0.0699337 0.0187556 3.729
spqualityB+ 0.0978148 0.0181447 5.391
spqualityC 0.1736531 0.0199029 8.725
spqualityD 0.3608247 0.0373088 9.671
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divta 0.5490122 0.1776610 3.090
cashta -0.2229544 0.0346485 -6.435
factor(industry)Bus-eq -0.1053724 0.0189318 -5.566
factor(industry)Chem -0.0501774 0.0238176 -2.107
factor(industry)Durbl -0.0709785 0.0247872 -2.864
factor(industry)Enrgy -0.0899567 0.0386883 -2.325
factor(industry)Fin 0.0028891 0.0208928 0.138
factor(industry)Hlth -0.0724094 0.0214998 -3.368
factor(industry)Manuf -0.0588759 0.0232521 -2.532
factor(industry)NoDur -0.0597369 0.0255610 -2.337
factor(industry)Shops -0.0782346 0.0201570 -3.881
factor(industry)Telcm 0.0558288 0.0391838 1.425
Pr(>|t|) (Intercept) 6.69e-13 ***
logassets 0.006594 ** capexta 0.153149 rdta 2.68e-10 ***
taxes 0.481913 spqualityA- 0.080323 . spqualityA+ 0.982474 spqualityB 1.84e-05 ***
spqualityB- 0.000197 ***
spqualityB+ 7.73e-08 ***
spqualityC < 2e-16 ***
spqualityD < 2e-16 ***
divta 0.002024 ** cashta 1.50e-10 ***
factor(industry)Bus-eq 2.91e-08 ***
factor(industry)Chem 0.035248 * factor(industry)Durbl 0.004227 ** factor(industry)Enrgy 0.020149 * factor(industry)Fin 0.890031 factor(industry)Hlth 0.000770 ***
factor(industry)Manuf 0.011405 * factor(industry)NoDur 0.019523 * factor(industry)Shops 0.000107 ***
factor(industry)Telcm 0.154352 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.181 on 2314 degrees of freedom
(4662 observations deleted due to missingness)
Multiple R-squared: 0.2262,
Adjusted R-squared: 0.2186
F-statistic: 29.42 on 23 and 2314 DF, p-value: < 2.2e-16
> mean((test$leverage-predict(lm.fit6, test))^2)
Error in eval(predvars, data, env) : object 'capexta' not found
> #Logisitc Regression > #simple logistic
> glm.fit <- glm(leverageincrease~logassets, family=binomial, data=capstr)
> summary(glm.fit)
Call:
glm(formula = leverageincrease ~ logassets, family = binomial, data = capstr)
Deviance Residuals: Min 1Q Median 3Q Max -0.6956 -0.6610 -0.6528 -0.6454 1.8305 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) -1.65714 0.23668 -7.002 2.53e-12 ***
logassets 0.02735 0.02707 1.010 0.312 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.1 on 5633 degrees of freedom
Residual deviance: 5551.1 on 5632 degrees of freedom
AIC: 5555.1
Number of Fisher Scoring iterations: 4
> #multiple logistic
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, data=capstr)
> summary(glm.fit)
Call:
glm(formula = leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, family = binomial, data = capstr)
Deviance Residuals: Min 1Q Median 3Q Max
-1.1002 -0.6740 -0.6298 -0.5868 1.9781 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) -1.973817 0.300742 -6.563 5.27e-11 ***
logassets 0.045184 0.028067 1.610 0.10742 capexta 3.492695 1.102446 3.168 0.00153 ** rdta 1.130905 0.742120 1.524 0.12754 taxes -0.132474 5.417023 -0.024 0.98049 spqualityA- -0.194172 0.183344 -1.059 0.28957 spqualityA+ 0.270778 0.238488 1.135 0.25621 spqualityB -0.064246 0.154990 -0.415 0.67850 spqualityB- 0.008132 0.155342 0.052 0.95825 spqualityB+ -0.159035 0.154894 -1.027 0.30454 spqualityC 0.143413 0.163208 0.879 0.37956 spqualityD 0.363117 0.294022 1.235 0.21683 divta 1.339934 0.922925 1.452 0.14655 cashta 0.170486 0.286316 0.595 0.55155 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.1 on 5633 degrees of freedom
Residual deviance: 5520.1 on 5620 degrees of freedom
AIC: 5548.1
Number of Fisher Scoring iterations: 4
> #Get predictions on whether market will go up or down
> # First code everything as Down
> glm.pred = rep("0",5634)
> # Recode probabilities greater than .5 as up
> glm.probs<-predict(glm.fit,capstr,type="response")
> glm.pred[glm.probs>.5]="1"
> table(glm.pred,capstr$leverageincrease)
glm.pred 0 1
0 4538 1095
1 0 1
> mean(glm.pred==capstr$leverageincrease)
[1] 0.8056443
> #Fit a logistic model on training dataset
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> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> glm.probs<-predict(glm.fit,test,type="response")
Error in eval(predvars, data, env) : object 'capexta' not found
> glm.pred=rep("0",3191)
> glm.pred[glm.probs>.5]="1"
> mean(glm.pred==test$leverageincrease)
[1] NaN
> #Fit a logistic model on training dataset
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> glm.probs<-predict(glm.fit,test,type="response")
Error in eval(predvars, data, env) : object 'capexta' not found
> library(ISLR2)
> library(MASS)
> library(car)
Error in library(car) : there is no package called ‘car’
> library(boot)
> library(class)
> #Fit a logistic model on training dataset
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> glm.probs<-predict(glm.fit,test,type="response")
Error in eval(predvars, data, env) : object 'capexta' not found
> #Add year and industry effects
> lm.fit6 <- lm(leverage~logassets+capexta+rdta+taxes+spquality+divta+cashta+factor(industry),
data=capstr,subset=train)
> summary(lm.fit6)
Call:
lm(formula = leverage ~ logassets + capexta + rdta + taxes + spquality + divta + cashta + factor(industry), data = capstr, subset = train)
Residuals:
Min 1Q Median 3Q Max -0.44866 -0.11462 -0.01504 0.09621 1.33151 Coefficients:
Estimate Std. Error t value
(Intercept) 0.2845002 0.0393679 7.227
logassets 0.0088708 0.0032623 2.719
capexta -0.2056597 0.1439220 -1.429
rdta -0.6576442 0.1036640 -6.344
taxes -0.4173570 0.5933910 -0.703
spqualityA- 0.0365232 0.0208753 1.750
spqualityA+ -0.0006213 0.0282817 -0.022
spqualityB 0.0792077 0.0184534 4.292
spqualityB- 0.0699337 0.0187556 3.729
spqualityB+ 0.0978148 0.0181447 5.391
spqualityC 0.1736531 0.0199029 8.725
spqualityD 0.3608247 0.0373088 9.671
divta 0.5490122 0.1776610 3.090
cashta -0.2229544 0.0346485 -6.435
factor(industry)Bus-eq -0.1053724 0.0189318 -5.566
factor(industry)Chem -0.0501774 0.0238176 -2.107
factor(industry)Durbl -0.0709785 0.0247872 -2.864
factor(industry)Enrgy -0.0899567 0.0386883 -2.325
factor(industry)Fin 0.0028891 0.0208928 0.138
factor(industry)Hlth -0.0724094 0.0214998 -3.368
factor(industry)Manuf -0.0588759 0.0232521 -2.532
factor(industry)NoDur -0.0597369 0.0255610 -2.337
factor(industry)Shops -0.0782346 0.0201570 -3.881
factor(industry)Telcm 0.0558288 0.0391838 1.425
Pr(>|t|) (Intercept) 6.69e-13 ***
logassets 0.006594 ** capexta 0.153149 rdta 2.68e-10 ***
taxes 0.481913 spqualityA- 0.080323 . spqualityA+ 0.982474 spqualityB 1.84e-05 ***
spqualityB- 0.000197 ***
spqualityB+ 7.73e-08 ***
spqualityC < 2e-16 ***
spqualityD < 2e-16 ***
divta 0.002024 ** cashta 1.50e-10 ***
factor(industry)Bus-eq 2.91e-08 ***
factor(industry)Chem 0.035248 * factor(industry)Durbl 0.004227 ** factor(industry)Enrgy 0.020149 * factor(industry)Fin 0.890031 factor(industry)Hlth 0.000770 ***
factor(industry)Manuf 0.011405 * factor(industry)NoDur 0.019523 * factor(industry)Shops 0.000107 ***
factor(industry)Telcm 0.154352 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.181 on 2314 degrees of freedom
(4662 observations deleted due to missingness)
Multiple R-squared: 0.2262,
Adjusted R-squared: 0.2186 F-statistic: 29.42 on 23 and 2314 DF, p-value: < 2.2e-16
> mean((test$leverage-predict(lm.fit6, test))^2)
Error in eval(predvars, data, env) : object 'capexta' not found
> #Logisitc Regression > #simple logistic
> glm.fit <- glm(leverageincrease~logassets, family=binomial, data=capstr)
> summary(glm.fit)
Call:
glm(formula = leverageincrease ~ logassets, family = binomial, data = capstr)
Deviance Residuals: Min 1Q Median 3Q Max -0.6956 -0.6610 -0.6528 -0.6454 1.8305 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) -1.65714 0.23668 -7.002 2.53e-12 ***
logassets 0.02735 0.02707 1.010 0.312 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.1 on 5633 degrees of freedom
Residual deviance: 5551.1 on 5632 degrees of freedom
AIC: 5555.1
Number of Fisher Scoring iterations: 4
> #multiple logistic
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, data=capstr)
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> summary(glm.fit)
Call:
glm(formula = leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, family = binomial, data = capstr)
Deviance Residuals: Min 1Q Median 3Q Max -1.1002 -0.6740 -0.6298 -0.5868 1.9781 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) -1.973817 0.300742 -6.563 5.27e-11 ***
logassets 0.045184 0.028067 1.610 0.10742 capexta 3.492695 1.102446 3.168 0.00153 ** rdta 1.130905 0.742120 1.524 0.12754 taxes -0.132474 5.417023 -0.024 0.98049 spqualityA- -0.194172 0.183344 -1.059 0.28957 spqualityA+ 0.270778 0.238488 1.135 0.25621 spqualityB -0.064246 0.154990 -0.415 0.67850 spqualityB- 0.008132 0.155342 0.052 0.95825 spqualityB+ -0.159035 0.154894 -1.027 0.30454 spqualityC 0.143413 0.163208 0.879 0.37956 spqualityD 0.363117 0.294022 1.235 0.21683 divta 1.339934 0.922925 1.452 0.14655 cashta 0.170486 0.286316 0.595 0.55155 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.1 on 5633 degrees of freedom
Residual deviance: 5520.1 on 5620 degrees of freedom
AIC: 5548.1
Number of Fisher Scoring iterations: 4
> #Get predictions on whether market will go up or down
> # First code everything as Down
> glm.pred = rep("0",5634)
> # Recode probabilities greater than .5 as up
> glm.probs<-predict(glm.fit,capstr,type="response")
> glm.pred[glm.probs>.5]="1"
> table(glm.pred,capstr$leverageincrease)
glm.pred 0 1
0 4538 1095
1 0 1
> mean(glm.pred==capstr$leverageincrease)
[1] 0.8056443
> #Fit a logistic model on training dataset
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> #Fit a logistic model on training dataset
> glm.fit <- glm(leverageincrease~logassets+rdta+taxes+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> glm.probs<-predict(glm.fit,test,type="response")
Error in eval(predvars, data, env) : object 'taxes' not found
> #Fit a logistic model on training dataset
> glm.fit <- glm(leverageincrease~logassets+rdta+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> glm.probs<-predict(glm.fit,test,type="response")
Error in eval(predvars, data, env) : object 'spquality' not found
> glm.probs<-predict(glm.fit,test,type="response")
Error in eval(predvars, data, env) : object 'spquality' not found
> glm.pred=rep("0",3191)
> glm.pred[glm.probs>.5]="1"
> mean(glm.pred==test$leverageincrease)
[1] NaN
> #Linear Discriminant Analysis
> lda.fit1 <- lda(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, data=capstr)
> lda.fit1
Call:
lda(leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, data = capstr)
Prior probabilities of groups:
0 1 0.8054668 0.1945332 Group means:
logassets capexta rdta taxes spqualityA-
0 8.620847 0.02826140 0.02841552 0.003660968 0.08241516
1 8.662744 0.03144299 0.03230833 0.003812621 0.07208029
spqualityA+ spqualityB spqualityB- spqualityB+ spqualityC
0 0.02269722 0.2194799 0.2170560 0.2322609 0.1542530
1 0.03193431 0.2107664 0.2198905 0.2025547 0.1806569
spqualityD divta cashta
0 0.01344204 0.02014315 0.1229749
1 0.01824818 0.02128598 0.1313459
Coefficients of linear discriminants:
LD1
logassets 0.23315524
capexta 19.18949555
rdta 6.50725922
taxes -2.15264353
spqualityA- -0.97400065
spqualityA+ 1.56080364
spqualityB -0.30678978
spqualityB- 0.07470397
spqualityB+ -0.78022105
spqualityC 0.81401206
spqualityD 2.05192296
divta 8.27987601
cashta 0.82615561
> plot(lda.fit1)
Error in plot.new() : figure margins too large
> lda.pred <- predict(lda.fit1,capstr)
> names(lda.pred)
[1] "class" "posterior" "x" > lda.class <- lda.pred$class
> table(lda.class, capstr$leverageincrease)
lda.class 0 1
0 4538 1094
1 0 2
> table(lda.class, capstr$leverageincrease)
lda.class 0 1
0 4538 1094
1 0 2
> mean(lda.class==capstr$leverageincrease)
[1] 0.8058218
> lda.fit2<- lda(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, data=capstr, subset=train)
> lda.fit2
Call:
lda(leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, data = capstr, subset = train)
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Prior probabilities of groups:
0 1 0.8028229 0.1971771 Group means:
logassets capexta rdta taxes spqualityA-
0 8.623723 0.02853900 0.02651503 0.003626550 0.08311135
1 8.696534 0.03031127 0.03444373 0.003849535 0.06507592
spqualityA+ spqualityB spqualityB- spqualityB+ spqualityC
0 0.02397443 0.2258924 0.2226958 0.2296217 0.1491742
1 0.03470716 0.1822126 0.2364425 0.2082430 0.1952278
spqualityD divta cashta
0 0.01331913 0.02021972 0.1193634
1 0.01084599 0.01828916 0.1312630
Coefficients of linear discriminants:
LD1
logassets 0.2966223
capexta 5.4377002
rdta 12.5297516
taxes 5.4496934
spqualityA- -1.7077322
spqualityA+ 0.7639195
spqualityB -1.7749926
spqualityB- -0.8510942
spqualityB+ -1.3590768
spqualityC -0.1672927
spqualityD -1.4752464
divta -10.9214691
cashta -0.4883071
> plot(lda.fit2)
Error in plot.new() : figure margins too large
> lda.pred<-predict(lda.fit2, test)
Error in eval(predvars, data, env) : object 'capexta' not found
> names(lda.pred)
[1] "class" "posterior" "x" > test.levinc <- test$leverageincrease
> lda.class<-lda.pred$class
> table(lda.class,test.levinc)
Error in table(lda.class, test.levinc) : all arguments must have the same length
> mean(lda.class==test.levinc)
[1] NaN
> attach(capstr)
The following objects are masked from ceo_comp:
gvkey, industry, leverage, logassets, rdta, roa,
year
> library(readxl)
> capstr <- read_excel("Desktop/capstr.xlsx")
> View(capstr) > library(ISLR2)
> library(MASS)
> library(car)
Error in library(car) : there is no package called ‘car’
> library(boot)
> library(class)
> # import data and clean
> capstr <- na.omit(capstr)
> dim(capstr)
[1] 5634 14
> names(capstr)
[1] "gvkey" "year" "conm" [4] "spquality" "industry" "leverage" [7] "logassets" "rdta" "cashta" [10] "divta" "taxes" "capexta" [13] "roa" "leverageincrease"
> #inspect your data
> mean(capstr$leverage)
[1] 0.3427896
> median(capstr$leverage)
[1] 0.3278918
> sd(capstr$leverage)
[1] 0.2064969
> #linear regression of leverage
> lm.fit1 <- lm(leverage~logassets, data=capstr)
> summary(lm.fit1)
Call:
lm(formula = leverage ~ logassets, data = capstr)
Residuals:
Min 1Q Median 3Q Max -0.36522 -0.14258 -0.01556 0.11545 1.50374 Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.250999 0.019425 12.922 < 2e-16 ***
logassets 0.010638 0.002228 4.773 1.86e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2061 on 5632 degrees of freedom
Multiple R-squared: 0.004029,
Adjusted R-squared: 0.003853 F-statistic: 22.79 on 1 and 5632 DF, p-value: 1.857e-06
> #training test split
> train<-(capstr$year<2018)
> test <- capstr[!train,]
> lm.fit3 <- lm(leverage~logassets, data=capstr, subset=train)
> mean((test$leverage-predict(lm.fit3, test))^2)
[1] 0.04393114
> #multiple regression
> lm.fit5 <- lm(leverage~logassets+capexta+rdta+taxes+spquality+divta+cashta, data=capstr, subset=train)
> summary(lm.fit5)
Call:
lm(formula = leverage ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, data = capstr, subset = train)
Residuals:
Min 1Q Median 3Q Max -0.43731 -0.11904 -0.01312 0.09942 1.61583 Coefficients:
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.220487 0.033958 6.493 1.02e-10 ***
logassets 0.008460 0.003217 2.630 0.008594 ** capexta -0.595151 0.123316 -4.826 1.48e-06 ***
rdta -0.521944 0.092958 -5.615 2.19e-08 ***
taxes -1.661234 0.664315 -2.501 0.012461 * spqualityA- 0.077493 0.020388 3.801 0.000148 ***
spqualityA+ -0.012045 0.028820 -0.418 0.676034 spqualityB 0.097512 0.017649 5.525 3.64e-08 ***
spqualityB- 0.099913 0.017668 5.655 1.74e-08 ***
spqualityB+ 0.111681 0.017550 6.364 2.35e-10 ***
spqualityC 0.157216 0.018804 8.361 < 2e-16 ***
spqualityD 0.264586 0.030928 8.555 < 2e-16 ***
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divta 0.698880 0.133180 5.248 1.67e-07 ***
cashta -0.352665 0.032688 -10.789 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1847 on 2429 degrees of freedom
Multiple R-squared: 0.1743,
Adjusted R-squared: 0.1699 F-statistic: 39.44 on 13 and 2429 DF, p-value: < 2.2e-16
> mean((test$leverage-predict(lm.fit5, test))^2)
[1] 0.03657678
> #Add year and industry effects
> lm.fit6 <- lm(leverage~logassets+capexta+rdta+taxes+spquality+divta+cashta+factor(industry),
data=capstr,subset=train)
> summary(lm.fit6)
Call:
lm(formula = leverage ~ logassets + capexta + rdta + taxes + spquality + divta + cashta + factor(industry), data = capstr, subset = train)
Residuals:
Min 1Q Median 3Q Max -0.45878 -0.11077 -0.01682 0.09314 1.62986 Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.328070 0.038296 8.567 < 2e-16
logassets 0.006216 0.003209 1.937 0.052899
capexta -0.258067 0.136773 -1.887 0.059304
rdta -0.370863 0.096991 -3.824 0.000135
taxes -0.602740 0.664720 -0.907 0.364625
spqualityA- 0.061749 0.019961 3.094 0.002000
spqualityA+ -0.012442 0.028097 -0.443 0.657932
spqualityB 0.074368 0.017384 4.278 1.96e-05
spqualityB- 0.067537 0.017578 3.842 0.000125
spqualityB+ 0.092536 0.017186 5.385 7.96e-08
spqualityC 0.128479 0.018772 6.844 9.72e-12
spqualityD 0.249136 0.030222 8.244 2.71e-16
divta 0.468911 0.135039 3.472 0.000525
cashta -0.307321 0.032734 -9.388 < 2e-16
factor(industry)Bus-eq -0.124543 0.018648 -6.679 2.98e-11
factor(industry)Chem -0.051746 0.022961 -2.254 0.024309
factor(industry)Durbl -0.090336 0.024493 -3.688 0.000231
factor(industry)Enrgy -0.138919 0.036960 -3.759 0.000175
factor(industry)Fin -0.017993 0.019967 -0.901 0.367609
factor(industry)Hlth -0.071240 0.021143 -3.369 0.000765
factor(industry)Manuf -0.110165 0.022513 -4.893 1.06e-06
factor(industry)NoDur -0.092187 0.024685 -3.735 0.000192
factor(industry)Shops -0.131980 0.019895 -6.634 4.02e-11
factor(industry)Telcm 0.066267 0.035486 1.867 0.061962
(Intercept) ***
logassets . capexta . rdta ***
taxes spqualityA- ** spqualityA+ spqualityB ***
spqualityB- ***
spqualityB+ ***
spqualityC ***
spqualityD ***
divta ***
cashta ***
factor(industry)Bus-eq ***
factor(industry)Chem * factor(industry)Durbl ***
factor(industry)Enrgy ***
factor(industry)Fin factor(industry)Hlth ***
factor(industry)Manuf ***
factor(industry)NoDur ***
factor(industry)Shops ***
factor(industry)Telcm . ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1797 on 2419 degrees of freedom
Multiple R-squared: 0.2215,
Adjusted R-squared: 0.2141 F-statistic: 29.93 on 23 and 2419 DF, p-value: < 2.2e-16
> mean((test$leverage-predict(lm.fit6, test))^2)
[1] 0.0358012
> #Logisitc Regression
> #simple logistic
> glm.fit <- glm(leverageincrease~logassets, family=binomial, data=capstr)
> summary(glm.fit)
Call:
glm(formula = leverageincrease ~ logassets, family = binomial, data = capstr)
Deviance Residuals: Min 1Q Median 3Q Max -0.6956 -0.6610 -0.6528 -0.6454 1.8305 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) -1.65714 0.23668 -7.002 2.53e-12 ***
logassets 0.02735 0.02707 1.010 0.312 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.1 on 5633 degrees of freedom
Residual deviance: 5551.1 on 5632 degrees of freedom
AIC: 5555.1
Number of Fisher Scoring iterations: 4
> #multiple logistic
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, data=capstr)
> summary(glm.fit)
Call:
glm(formula = leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, family = binomial, data = capstr)
Deviance Residuals: Min 1Q Median 3Q Max -1.1002 -0.6740 -0.6298 -0.5868 1.9781 Coefficients:
Estimate Std. Error z value Pr(>|z|) (Intercept) -1.973817 0.300742 -6.563 5.27e-11 ***
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logassets 0.045184 0.028067 1.610 0.10742 capexta 3.492695 1.102446 3.168 0.00153 ** rdta 1.130905 0.742120 1.524 0.12754 taxes -0.132474 5.417023 -0.024 0.98049 spqualityA- -0.194172 0.183344 -1.059 0.28957 spqualityA+ 0.270778 0.238488 1.135 0.25621 spqualityB -0.064246 0.154990 -0.415 0.67850 spqualityB- 0.008132 0.155342 0.052 0.95825 spqualityB+ -0.159035 0.154894 -1.027 0.30454 spqualityC 0.143413 0.163208 0.879 0.37956 spqualityD 0.363117 0.294022 1.235 0.21683 divta 1.339934 0.922925 1.452 0.14655 cashta 0.170486 0.286316 0.595 0.55155 ---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.1 on 5633 degrees of freedom
Residual deviance: 5520.1 on 5620 degrees of freedom
AIC: 5548.1
Number of Fisher Scoring iterations: 4
> #Get predictions on whether market will go up or down
> # First code everything as Down
> glm.pred = rep("0",5634)
> # Recode probabilities greater than .5 as up
> glm.probs<-predict(glm.fit,capstr,type="response")
> glm.pred[glm.probs>.5]="1"
> table(glm.pred,capstr$leverageincrease)
glm.pred 0 1
0 4538 1095
1 0 1
> #Fit a logistic model on training dataset
> glm.fit <- glm(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, family=binomial, subset=train, data=capstr)
> glm.probs<-predict(glm.fit,test,type="response")
> glm.pred=rep("0",3191)
> glm.pred[glm.probs>.5]="1"
> mean(glm.pred==test$leverageincrease)
[1] 0.7586963
> #Linear Discriminant Analysis
> lda.fit1 <- lda(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, data=capstr)
> lda.fit1
Call:
lda(leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, data = capstr)
Prior probabilities of groups:
0 1 0.8054668 0.1945332 Group means:
logassets capexta rdta taxes spqualityA-
0 8.620847 0.02826140 0.02841552 0.003660968 0.08241516
1 8.662744 0.03144299 0.03230833 0.003812621 0.07208029
spqualityA+ spqualityB spqualityB- spqualityB+ spqualityC
0 0.02269722 0.2194799 0.2170560 0.2322609 0.1542530
1 0.03193431 0.2107664 0.2198905 0.2025547 0.1806569
spqualityD divta cashta
0 0.01344204 0.02014315 0.1229749
1 0.01824818 0.02128598 0.1313459
Coefficients of linear discriminants:
LD1
logassets 0.23315524
capexta 19.18949555
rdta 6.50725922
taxes -2.15264353
spqualityA- -0.97400065
spqualityA+ 1.56080364
spqualityB -0.30678978
spqualityB- 0.07470397
spqualityB+ -0.78022105
spqualityC 0.81401206
spqualityD 2.05192296
divta 8.27987601
cashta 0.82615561
> plot(lda.fit1)
Error in plot.new() : figure margins too large
> lda.pred <- predict(lda.fit1,capstr)
> names(lda.pred)
[1] "class" "posterior" "x" > lda.class <- lda.pred$class
> table(lda.class, capstr$leverageincrease)
lda.class 0 1
0 4538 1094
1 0 2
> mean(lda.class==capstr$leverageincrease)
[1] 0.8058218
> lda.fit2<- lda(leverageincrease~logassets+capexta+rdta+taxes+spquality+divta+cashta, data=capstr, subset=train)
> lda.fit2
Call:
lda(leverageincrease ~ logassets + capexta + rdta + taxes + spquality + divta + cashta, data = capstr, subset = train)
Prior probabilities of groups:
0 1 0.8665575 0.1334425 Group means:
logassets capexta rdta taxes spqualityA-
0 8.560676 0.03063772 0.02823171 0.003542609 0.07888521
1 8.588997 0.03405813 0.02995474 0.003885632 0.08588957
spqualityA+ spqualityB spqualityB- spqualityB+ spqualityC
0 0.02267359 0.2243741 0.2272083 0.2172886 0.1549362
1 0.03067485 0.1871166 0.2024540 0.2239264 0.1656442
spqualityD divta cashta
0 0.02031176 0.02069909 0.1212555
1 0.01840491 0.02140061 0.1267697
Coefficients of linear discriminants:
LD1
logassets 0.07437504
capexta 14.18858846
rdta 2.75013964
taxes 26.01643615
spqualityA- -2.09679273
spqualityA+ -0.80507013
spqualityB -3.25118683
spqualityB- -2.94930233
spqualityB+ -2.29109597
spqualityC -2.16343389
spqualityD -2.73205749
divta -0.33553702
cashta 0.78987199
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> plot(lda.fit2)
Error in plot.new() : figure margins too large
> lda.pred<-predict(lda.fit2, test)
> names(lda.pred)
[1] "class" "posterior" "x" > test.levinc <- test$leverageincrease
> lda.class<-lda.pred$class
> table(lda.class,test.levinc)
test.levinc
lda.class 0 1
0 2421 770
1 0 0
> mean(lda.class==test.levinc)
[1] 0.7586963
> attach(capstr)
The following objects are masked from capstr (pos = 4):
capexta, cashta, conm, divta, gvkey, industry,
leverage, leverageincrease, logassets, rdta, roa,
spquality, taxes, year
The following objects are masked from ceo_comp:
gvkey, industry, leverage, logassets, rdta, roa,
year
> train.X<-cbind(logassets, roa)[train,]
> test.X<-cbind(logassets, roa)[!train,]
> train.levinc=leverageincrease[train]
> test.levinc=leverageincrease[!train]
> knn.pred1<-knn(train.X,test.X,train.levinc,k=5)
> table(knn.pred,test.levinc)
Error in table(knn.pred, test.levinc) : all arguments must have the same length
> mean(knn.pred==test.levinc)
[1] 0
Warning messages:
1: In `==.default`(knn.pred, test.levinc) :
longer object length is not a multiple of shorter object length
2: In is.na(e1) | is.na(e2) :
longer object length is not a multiple of shorter object length
> lm.fit1 <- lm(leverage~logassets, data=capstr, subset=train)
> mean((test$leverage-predict(lm.fit1, test))^2)
[1] 0.04393114
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> lm.fit2 <- lm(leverage~poly(logassets,2), data=capstr, subset=train)
> mean((test$leverage-predict(lm.fit2, test))^2)
[1] 0.04301659
> lm.fit3 <- lm(leverage~poly(logassets,3), data=capstr, subset=train)
> mean((test$leverage-predict(lm.fit3,test))^2)
[1] 0.04300088
> length(train.X)
[1] 4886
> length(test.X)
[1] 6382
> length(train.levinc)
[1] 2443
> length(test.levinc)
[1] 3191
> split_ratio <- 0.7
> total_samples <- nrow(your_data)
Error in nrow(your_data) : object 'your_data' not found
> total_samples <- nrow(capstr)
> train_indices <- sample(1:total_samples, size = round(total_samples * split_ratio))
> train.X<-cbind(logassets, roa)[train,]
> test.X<-cbind(logassets, roa)[!train,]
> train.levinc=leverageincrease[train]
> test.levinc=leverageincrease[!train]
> knn.pred1<-knn(train.X,test.X,train.levinc,k=5)
> table(knn.pred,test.levinc)
Error in table(knn.pred, test.levinc) : all arguments must have the same length
> length(train.X)
[1] 4886
> length(test.X)
[1] 6382
> length(train.levinc)
[1] 2443
> length(test.levinc)
[1] 3191
> split_ratio <- 0.7
> total_samples <- nrow(capstr)
> train.X <- cbind(logassets, roa)[train, ]
> test.X <- cbind(logassets, roa)[!train, ]
> train.levinc = leverageincrease[train]
> test.levinc = leverageincrease[!train]
> knn.pred1 <- knn(train.X, test.X, train.levinc, k = 5)
> confusion_matrix <- table(knn.pred1, test.levinc)
> accuracy <- mean(knn.pred1 == test.levinc)
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> confusion_matrix
test.levinc
knn.pred1 0 1
0 2385 748
1 36 22
> accuracy
[1] 0.754309
>
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- ALEKS - Christian Seither - Learn X + ● https://www-awu.aleks.com/alekscgi/x/Isl.exe/10_u-IgNslkr7j8P3jH-1BjnuwZGiweF Here are the meanings of some of the symbols that appear in the statements belo means "is a subset of." C means "is a proper subset of." Z means "is not a subset of." Øis the empty set. For each statement, decide if it is true or false. . SETS Identifying true statements involving subsets and proper subsets Statement (11, 13, 15) Jxplanation Check (11, 12, 13, 14, 15} (7,9) Ø (c. d. f. g} = (d, f} (q, r, w) C (q, r, w} True False O 0 O O O Search X hparrow_forwardThe name of a variable in the new programming language K is a string that can contain upper case letters, lowercase letters, digits or underscores. Further, the first character in the string must be a letter, either uppercase or lower case or an underscore. If the name of a variable is determined by its eleven characters, how many different variables can be named in this programming language? ( Note: a name of a variable may contain fewer than eleven charactersarrow_forwardHelppppppp::/$;$;&(&(&(&;&;&;&&&;&;&(&(&;&;&(&(&(&;@;&((&;:&:@(&(&;&@;arrow_forward
- 3) That is everything please help, thank youarrow_forwardThe name of a variable in the F programming language is a string that can contain uppercase letters, lowercase letters, digits or underscores. Further, the first charcter in the string must be a letter, either uppercase or lowercase or an underscore. If the name of a variable is determined by the fiirst nine characters, how many different variables can be named?arrow_forwardConsider the diagram to the right below and complete the proof below. Given: BA = DC ZBAC = LDCA А, Prove: BC = DA D' Statements Reasons 1. BA = DC 1. Given ZBAC = LDCA 2. AC = TA 2. 3. ABCA = ADAC 3. 4. BC = DA Which of the following complete the proof above? B.arrow_forward
- Part 2 Multiple Choice. For each of the following strings of symbols, write in the corresponding space: "A" if the string of symbols is not a WFF in SL; "B" if the string of symbols is WFF in SL, but it is ambiguous (assuming parentheses dropping conventions); and " if the string of symbols is a WFF that is unambiguous (given parentheses dropping conventions). 1. P->(Qv(C&S)) 2. (P→Q→R)&~S 3. ((FG)→(TvW&Z)) 4. T&P→>(GvS) 5. (R>Rv~Karrow_forwardSuppose each license plate in a certain state has two digits, followed by two letters, followed by two digits. The letters O and U are not used. So, there are 24 letters and 10 digits that are used. Assume that the letters and digits can be repeated. How many license plates can be generated using this format? Espa license plates I Don't Know Submit O 2021 McGraw-Hill Education. All Rights Reserved. Terms of Use Privacy Accessibility P Type here to search 7:53 PM 3/11/2021 PSon f1 12 13 15 f6 f7 19 F10 f11 f12 prt sc sysrq pause break delete home insert 3arrow_forwardA bag contains four red marbles, three green ones, one lavender one, three yellows, and two orange marbles. HINT [See Example 7.] How many sets of five marbles include at least three red ones? -----------------------------setsarrow_forward
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