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2.a.)
> f<-read.csv("fish.csv",header=T)
> attach(f)
> m1<-glm(count~persons+child+factor(camper),family=poisson)
> summary(m1)

Call: glm(formula = count ~ persons + child + factor(camper), family = poisson)

Deviance Residuals: Min 1Q Median 3Q Max
-6.8096 -1.4431 -0.9060 -0.0406 16.1417

Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.98183 0.15226 -13.02 <2e-16 *** persons 1.09126 0.03926 27.80 <2e-16 *** child -1.68996 0.08099 -20.87 <2e-16 *** factor(camper)1 0.93094 0.08909 10.45 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 2958.4 on 249 degrees of freedom
Residual deviance: 1337.1 on 246 degrees of freedom
AIC: 1682.1

>plot(ftv,res1,ylim=c(-7,17),xlab="Fitted Values",ylab="Deviance Residuals",main="Deviance Residuals-Posiion Model")
> qqnorm(res1)

Number of Fisher Scoring iterations: 6

> round(cbind(exp(m1$coeff),exp(cbind(m1$coeff-qnorm(0.975)*sqrt(diag(vcov(m1))),m1$coeff+qnorm(0.975)*sqrt(diag(vcov(m1)))))),2) [,1] [,2] [,3]
(Intercept) 0.14 0.10 0.19 persons 2.98 2.76 3.22 child 0.18 0.16 0.22 factor(camper)1 2.54 2.13 3.02

b)
> res1<-residuals.glm(m1,"deviance")
> ftv<-m1$fitted.values plot(ftv,res1,ylim=c(-7,17),xlab="Fitted Values",ylab="Deviance Residuals",main="Deviance Residuals-Posiion Model")

c) round( cbind(
+ unlist(lapply(split(count, factor(camper):factor(child)),mean)),
+ unlist(lapply(split(count, factor(camper):factor(child)),var)),
+ unlist(lapply(split(count, factor(camper):factor(persons)),mean)),
+ unlist(lapply(split(count, factor(camper):factor(persons)),var))),2) [,1] [,2] [,3] [,4]
0:0 2.17 22.22 0.45 0.83
0:1 1.40 31.83 0.90 3.24
0:2 0.00 0.00 3.14 54.73
0:3 0.00 0.00 1.77 28.38
1:0 7.22 374.04 0.91 2.49
1:1 2.00 12.32 1.88 20.86
1:2 0.41 1.51 2.81 33.08
1:3 0.00 0.00 13.06 751.06

d)
> disp<-m1$dev/m1$df.res
> disp
[1] 5.435283

e) m2<-glm.nb(count ~ (persons) + (child) + factor(camper), link=log,init.theta=1,trace=T)
Theta(1) = 0.464595, 2(Ls - Lm) = 210.928000
Theta(2) = 0.463534, 2(Ls - Lm) = 210.654000
Theta(3) = 0.463533, 2(Ls - Lm) = 210.654000
Theta(4) = 0.463529, 2(Ls - Lm) = 210.653000
Theta(5) = 0.463529, 2(Ls - Lm) = 210.653000
Theta(6) = 0.463529, 2(Ls - Lm) = 210.653000
Theta(7) = 0.463529, 2(Ls - Lm) = 210.653000
> summary(m2)

Call: glm.nb(formula = count ~ (persons) + (child) + factor(camper), trace = T, init.theta = 0.4635287656, link = log)

Deviance Residuals: Min 1Q Median 3Q Max
-1.6673 -0.9599 -0.6590 -0.0319 4.9433

Coefficients: Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.6250 0.3304 -4.918 8.74e-07 *** persons 1.0608 0.1144 9.273 < 2e-16 *** child -1.7805 0.1850 -9.623 < 2e-16 *** factor(camper)1 0.6211 0.2348 2.645 0.00816 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(0.4635) family taken to be 1)

Null deviance: 394.25 on 249 degrees of freedom
Residual deviance: 210.65 on 246 degrees of freedom
AIC: 820.44

Number of Fisher Scoring iterations: 1

Theta: 0.4635 Std. Err.: 0.0712

2 x log-likelihood: -810.4440

> round(cbind(
+ m1$coeff,
+ exp(m1$coeff),
+ exp(m1$coeff - qnorm(.975)*sqrt(diag(vcov(m1)))),
+ exp(m1$coeff + qnorm(.975)*sqrt(diag(vcov(m1)))),
+ exp(m1$coeff - qnorm(.975)*sqrt(disp*diag(vcov(m1)))),
+ exp(m1$coeff + qnorm(.975)*sqrt(disp*diag(vcov(m1)))),
+ exp(m2$coeff),
+ exp(m2$coeff-qnorm(.975)*sqrt(diag(vcov(m2)))),
+ exp(m2$coeff+qnorm(.975)*sqrt(diag(vcov(m2))))
+ ),2) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
(Intercept) -1.98 0.14 0.10 0.19 0.07 0.28 0.20 0.10 0.38 persons 1.09 2.98 2.76 3.22 2.49 3.56 2.89 2.31 3.61 child -1.69 0.18 0.16 0.22 0.13 0.27 0.17 0.12 0.24 factor(camper)1 0.93 2.54 2.13 3.02 1.69 3.81 1.86 1.17 2.95

f)
> res2 <- residuals.glm(m2,"deviance")
> ftv2 <- m2$fitted.values

> plot(log(ftv2),rd2,ylim=c(-7,17), xlab="Log Fitted Values",
+ ylab="Deviance Residuals", main="Deviance Residuals
+ - Negative Binomial Model")

1. a)

> a<-read.table("handmade_q1.txt",header=TRUE)

> a$af<-factor(a$a)

> a$aft<-C(a$af,treatment)

> s$bf<-factor(a$b)

> a$bft<-C(a$bf,treatment)

> a$cf<-factor(a$c)

> a$cft<-C(a$cf,treatment)

> m1<-glm(y~aft+bft+cft+aft*bft+aft*cft+bft*cft,family=poisson,data=a)

summary(m1)

Call:

glm(formula = y ~ aft + bft + cft + aft * bft + aft * cft + bft *

cft, family = poisson, data = a)

Deviance Residuals:

Min 1Q Median 3Q Max

-1.65371 -0.54111 -0.01678 0.35203 2.21633

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) 7.517275 0.023292 322.747 < 2e-16 ***

aft2 -0.109903 0.033861 -3.246 0.00117 **

aft3 0.008339 0.032821 0.254 0.79945

aft4 0.243789 0.031032 7.856 3.96e-15 ***

aft5 -0.037687 0.033109 -1.138 0.25501

aft6 -0.070228 0.033322 -2.108 0.03507 *

aft7 -0.333295 0.035647 -9.350 < 2e-16 ***

aft8 -0.616834 0.038712 -15.934 < 2e-16 ***

aft9 -1.235275 0.047743 -25.874 < 2e-16 ***

bft1 -5.382773 0.255976 -21.028 < 2e-16 ***

cft1 -2.948221 0.102283 -28.824 < 2e-16 ***

aft2:bft1 0.677545 0.314142 2.157 0.03102 *

aft3:bft1 1.154825 0.284047 4.066 4.79e-05 ***

aft4:bft1 1.675248 0.268977 6.228 4.72e-10 ***

aft5:bft1 2.005658 0.266804 7.517 5.59e-14 ***

aft6:bft1 2.380827 0.263381 9.039 < 2e-16 ***

aft7:bft1 3.009812 0.262071 11.485 < 2e-16 ***

aft8:bft1 3.320893 0.262549 12.649 < 2e-16 ***

aft9:bft1 3.676959 0.265710 13.838 < 2e-16 ***

aft2:cft1 0.249583 0.139274 1.792 0.07313 .

aft3:cft1 0.643230 0.125942 5.107 3.27e-07 ***

aft4:cft1 0.772910 0.118701 6.511 7.45e-11 ***

aft5:cft1 1.101598 0.118318 9.311 < 2e-16 ***

aft6:cft1 1.273264 0.116233 10.954 < 2e-16 ***

aft7:cft1 1.289123 0.118159 10.910 < 2e-16 ***

aft8:cft1 1.342528 0.120780 11.115 < 2e-16 ***

aft9:cft1 1.479568 0.128754 11.491 < 2e-16 ***

bft1:cft1 2.834892 0.055976 50.645 < 2e-16 ***

---

1Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 25889.47 on 35 degrees of freedom

Residual deviance: 26.69 on 8 degrees of freedom

AIC: 338.21

Number of Fisher Scoring iterations: 4

1-pchisq(26.690,8)

[1] 0.0007995879

> m2<-glm(y~aft*bft*cft,family=poisson,data=a)

summary(m2)

Call:

glm(formula = y ~ aft * bft * cft, family = poisson, data = a)

Deviance Residuals:

[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[28] 0 0 0 0 0 0 0 0 0

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) 7.51806 0.02331 322.577 < 2e-16 ***

aft2 -0.10711 0.03388 -3.162 0.00157 **

aft3 0.01188 0.03286 0.361 0.71774

aft4 0.24708 0.03110 7.944 1.96e-15 ***

aft5 -0.03482 0.03325 -1.047 0.29501

aft6 -0.07265 0.03358 -2.164 0.03049 *

aft7 -0.32965 0.03603 -9.148 < 2e-16 ***

aft8 -0.64387 0.03972 -16.212 < 2e-16 ***

aft9 -1.25276 0.04944 -25.339 < 2e-16 ***

bft1 -5.57215 0.37868 -14.715 < 2e-16 ***

cft1 -2.96419 0.10521 -28.174 < 2e-16 ***

aft2:bft1 0.35843 0.50509 0.710 0.47793

aft3:bft1 0.98665 0.44336 2.225 0.02606 *

aft4:bft1 1.67821 0.40578 4.136 3.54e-05 ***

aft5:bft1 2.07789 0.40309 5.155 2.54e-07 ***

aft6:bft1 2.60407 0.39414 6.607 3.92e-11 ***

aft7:bft1 3.14592 0.39077 8.051 8.24e-16 ***

aft8:bft1 3.72184 0.38860 9.577 < 2e-16 ***

aft9:bft1 3.97029 0.39336 10.093 < 2e-16 ***

aft2:cft1 0.20720 0.14559 1.423 0.15471

2aft3:cft1 0.61039 0.13136 4.647 3.37e-06 ***

aft4:cft1 0.74812 0.12404 6.031 1.62e-09 ***

aft5:cft1 1.09041 0.12367 8.817 < 2e-16 ***

aft6:cft1 1.29951 0.12141 10.704 < 2e-16 ***

aft7:cft1 1.27703 0.12612 10.125 < 2e-16 ***

aft8:cft1 1.50609 0.12864 11.708 < 2e-16 ***

aft9:cft1 1.58169 0.14334 11.035 < 2e-16 ***

bft1:cft1 3.21550 0.51482 6.246 4.21e-10 ***

aft2:bft1:cft1 0.47976 0.65556 0.732 0.46427

aft3:bft1:cft1 0.18284 0.58513 0.312 0.75468

aft4:bft1:cft1 -0.07484 0.54631 -0.137 0.89103

aft5:bft1:cft1 -0.20081 0.54194 -0.371 0.71097

aft6:bft1:cft1 -0.43345 0.53272 -0.814 0.41584

aft7:bft1:cft1 -0.28911 0.53000 -0.545 0.58542

aft8:bft1:cft1 -0.77493 0.52873 -1.466 0.14275

aft9:bft1:cft1 -0.57755 0.53538 -1.079 0.28070

---

Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 2.5889e+04 on 35 degrees of freedom

Residual deviance: -5.7154e-13 on 0 degrees of freedom

AIC: 327.52

Number of Fisher Scoring iterations: 3

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...Clara Arias Business Statistics February 1, 2016 Nielsen Reflection While exploring Nielsen I realized the importance of knowing what we as consumers watch and buy. I personally don’t really watch TV at all; probably just a couple of shows but TV is not essential in my life. When I clicked on “Cable Network TV” I first saw these two programs called “Gold Rush” and “The Oreilly Factor” then the only thing I did was looked up these programs and read something about them since I didn’t really know about their existence. It’s probably unbelievable to you hearing this from me because nowadays almost everybody watches TV and everyone is aware of what is in the news. While looking up about “Gold Rush” I noticed it wasn’t a new series, it had actually been released since 2010 and now it is composed of 6 episodes. I think I should start watching TV since I felt I have been missing tons of stuff. In addition to this program I think it is essential to say that the network involved is “Disc”. I also went to look for most popular music and of course the first thing I saw was Justin Bieber with his song “Be yourself”, I usually listen to this song almost everyday because it is actually popular, but after knowing it is in the first place of ranking list I couldn’t help the craving of knowing how many reproductions it has on Youtube. Well it has about 247,768,905 reproductions in just 3 months, isn’t that crazy? I guess people are not surprised anymore about Justin’s fame. Another...

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...CASES DISPOSED, APPEALED, AND REVERSED IN HAMILTON COUNTY COURTS Common Pleas Court Judge Fred Cartolano Thomas Crush Patrick Dinkelacker Timothy Hogan Robert Kraft William Mathews William Morrissey Norbert Nadel Arthur Ney, Jr. Richard Niehaus Thomas Nurre John O� Connor Robert Ruehlman J. Howard Sundermann Ann Marie Tracey Ralph Winkler Total Total Cases Disposed 3,037 3,372 1,258 1,954 3,138 2,264 3,032 2,959 3,219 3,353 3,000 2,969 3,205 955 3,141 3,089 43,945 Appealed Cases 137 119 44 60 127 91 121 131 125 137 121 129 145 60 127 88 1,762 Reversed Cases 12 10 8 7 7 18 22 20 14 16 6 12 18 10 13 6 199 Common Pleas Court disposed 43, 945 total cases. The total number of cases appealed was 1,762, and the total number of cases reversed was 199. In all cases disposed in the Common Pleas Court, the probability of cases could be appealed and reversed is? Total reversed cases/ Total appealed cases= 199/1762= 0.11294 or 11.2% Domestic Relations court disposed a total of 30,499 cases. The total number of cases appealed was 106, and the total number of cases reversed was 17. In all cases disposed in the Domestic Relations Court, the probability of cases could be appealed and reversed is: Total reversed cases/ Total appealed cases=17/106= 0.16037 or 16% Municipal Court disposed of a total of 108,464. The total number of cases they appealed was 500, and the total number of cases reversed was 104. In all cases disposed in the Municipal Court, the probability of cases could be...

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...BUAD 310 – Spring 2011 - Dr. Arif Ansari Topics Covered –Simple Regression Homework # 4 - 100 points (Due date 4/4/2011- Monday) For Home Work 4, Turn in Part 1 (15 points), Question 1(20 points), Question 2 (20 points), Question 3 45 points). Part 1 MULTIPLE CHOICE [3 point each] 1. In Least squares regression, the regression line is obtained by minimizing, a) The total variation in the dependent variable. b) The sum of squares for error (SSE). c) The sum of squares for regression (SSR) d) The sum of squares for total (SST). e) None of the above 2. In a simple regression analysis involving 25 data points, the standard error of estimate is calculated as S( = 2.0 and the Fts = 10, then the information from regression line (SSR) should be, a) 60 b) 50 c) 40 d) 30 e) None of the above 3. In a statistics course, a linear regression equation was computed to predict the final exam score from the first quiz score. The equation obtained was Y = 10 + 0.9 X, where Y is the final exam score and X is the first quiz score. A prediction interval for Al Bundy who scored 95 on the first quiz and on the final exam scored 98 was computed. Also a confidence interval for mean score of 95 on the first quiz was computed. From this we can conclude: a) Al Bundy’s prediction interval in wider than the confidence interval. b) Al Bundy’s prediction interval in shorter than the confidence interval...

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...Factors that Affect Credit Score? FICO makes the formulas and programs for all credit reporting agencies. The names of formulas and actual procedures are different from agency to agency, the basic factors affecting credit score are however the same and the basic formula and its constituents remain the same. The three different models for credit scoring by FICO include, BEACON score used by Equifax, Experian/Fair Isaac Risk Model used by Experian and EMPIRICA used by TransUnion. The companies do not disclose the exact formulas but as per FICO resources, the following are the things that make up a credit score and also tend to affect the score. * Payment History (35%): The payment history basically consists of all your past accounts and the regularity with which payments have been made. A bad and irregular payment history causes the score to drop down. * Amounts Owed (30%): The total amount of debts owed to other lenders is also an important consideration in the score calculation. The standard equation is, more the amounts owed, less is the credit score. Hence keep the credit history and current liabilities to the bare minimum. * Length of Credit History (15%): The length of the credit history is also considered. Rule of the thumb is that longer the history, lesser is the score. Thus avoid unnecessary borrowings and keep them to the bare minimum. * New Credit (10%): New credit consists of the newly borrowed loans or newly taken up credit cards. Keeping it small always helps, as...

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