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Stats Homework (R) Part 1 of 2 Read section 11 of handbook_statsV13 What is the difference between these two models? g1 = glm(admit ~., data=mydata) g2 = glm(admit ~., data=mydata, family=binomial) Compute MSE (mean squared error) mean((g1$fitted.values mydata$admit)^2) mean((g2$fitted.values mydata$admit)^2) Which model is better in terms of MSE

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Stats Homework (R) Part 2 of 2 Consider two loss functions MSE.loss = function(y, yhat) mean((y - yhat)^2) log.loss = function(y, yhat) -mean(y * log(yhat) + (1-y) * log(1-yhat)) Which model (g1 or g2) is better in terms of log.loss? Hint: Compare log.loss(mydata$admit, g1$fitted.values) with log.loss(mydata$admit, g2$fitted.values) Hint: log.loss assumes yhat is a probability between 0 and 1 What are range(g1$fitted.values) and range(g2$fitted.values)? Let s = g1$fitted.values > 0 & g1$fitted.values < 1 What is log.loss(mydata$admit[s], g1$fitted.values[s])? Let baseline.fit be rep(mean(admit), length(admit)) How do the two models above compare to this baseline Compare both g1 and g2 to this baseline using both loss functions

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Functions fact = function(x) if(x < 2) 1 else x*fact(x-1) fact(5) fact2 = function(x) gamma(x+1) fact(5) fact(1:5) fact(seq(1,5,0.5))

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help(swiss)

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What are statistics packages good for? Plotting Scatter plots, histograms, boxplots Visualization Dendrograms, heatmaps Modeling Linear Regression Logistic Regression Hypothesis Testing

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Objects Data Types Numbers: 1, 1.5 Strings Functions: sqrt, help, summary Vectors: 3:30 c(1:5, 25:30) rnorm(100, 0, 1), rbinom(100, 10,.5) rep(0,10) scan( filename, 0) Matrices matrix(rep(0,100), ncol=10) diag(rep(1,10)) cbind(1:10, 21:30) rbind(1:10, 21:30) Data Frames swiss read.table (filename, header=T) Operations All: summary, help, print, cat Numbers: +,*,sqrt Strings: grep, substr, paste Vectors: x = (3:30) x+5 plot(x) mean(x), var(x), median(x) mean((x mean(x))^2) x[3], x[3:6], x[-1], x[x>20] Matrices: m = matrix(1:100,ncol=10) m+3, m* 3, m %*% m m[3,3], m[1:3,1:3], m[3,], m[m < 10] diag(m), t(m) Data Frames names(swiss) plot(swiss$Education, swiss$Fertility) plot(swiss[,1], swiss[,2]) pairs(swiss)

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plot(swiss$Education, swiss$Fertility)

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plot(swiss$Education, swiss$Fertility, col = 3 + (swiss$Catholic > 50))

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boxplot(split(swiss$Fertility, swiss$Catholic > 50))

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boxplot(split(swiss$Fertility, swiss$Education > median(swiss$Education)))

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pairs(swiss)

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Correlations > cor(swiss$Fertility, swiss$Catholic) [1] 0.4636847 > cor(swiss$Fertility, swiss$Education) [1] -0.6637889 > round(100*cor(swiss)) Fertility Agriculture Examination Education Catholic Infant.Mortality Fertility 100 35 -65 -66 46 42 Agriculture 35 100 -69 -64 40 -6 Examination -65 -69 100 70 -57 -11 Education -66 -64 70 100 -15 -10 Catholic 46 40 -57 -15 100 18 Infant.Mortality 42 -6 -11 -10 18 100 Many functions in R are polymorphic: cor works on vectors as well as matrices

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Regression > plot(swiss$Education, swiss$Fertility) > g = glm(swiss$Fertility ~ swiss$Education) > abline(g) > summary(g) Call: glm(formula = swiss$Fertility ~ swiss$Education) Deviance Residuals: Min 1Q Median 3Q Max -17.036 -6.711 -1.011 9.526 19.689 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 79.6101 2.1041 37.836 < 2e-16 *** swiss$Education -0.8624 0.1448 -5.954 3.66e-07 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 (Dispersion parameter for gaussian family taken to be 89.22746) Null deviance: 7178.0 on 46 degrees of freedom Residual deviance: 4015.2 on 45 degrees of freedom AIC: 348.42 Number of Fisher Scoring iterations: 2

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plot(swiss$Education, swiss$Fertility, type='n); abline(g) text(swiss$Education, swiss$Fertility, dimnames(swiss)[[1]])

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g = glm(Fertility ~., data=swiss); summary(g) Call: glm(formula = Fertility ~., data = swiss) Deviance Residuals: Min 1Q Median 3Q Max -15.2743 -5.2617 0.5032 4.1198 15.3213 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 66.91518 10.70604 6.250 1.91e-07 *** Agriculture -0.17211 0.07030 -2.448 0.01873 * Examination -0.25801 0.25388 -1.016 0.31546 Education -0.87094 0.18303 -4.758 2.43e-05 *** Catholic 0.10412 0.03526 2.953 0.00519 ** Infant.Mortality 1.07705 0.38172 2.822 0.00734 ** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 (Dispersion parameter for gaussian family taken to be 51.34251) Null deviance: 7178.0 on 46 degrees of freedom Residual deviance: 2105.0 on 41 degrees of freedom AIC: 326.07 Number of Fisher Scoring iterations: 2

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http://www.nytimes.com/2009/01/07/technology/business-computing/07program.html

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Plot Example help(ldeaths) plot(mdeaths, col="blue", ylab="Deaths", sub="Male (blue), Female (pink)", ylim=range(c(mdeaths, fdeaths))) lines(fdeaths, lwd=3, col="pink") abline(v=1970:1980, lty=3) abline(h=seq(0,3000,1000), lty=3, col="red")

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Periodicity plot(1:length(fdeaths), fdeaths, type='l') lines((1:length(fdeaths))+12, fdeaths, lty=3)

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Type Argument par(mfrow=c(2,2)) plot(fdeaths, type='p', main="points") plot(fdeaths, type='l', main="lines") plot(fdeaths, type='b', main="b") plot(fdeaths, type='o', main="o")

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Scatter Plot plot(as.vector(mdeaths), as.vector(fdeaths)) g=glm(fdeaths ~ mdeaths) abline(g) g$coef (Intercept) mdeaths -45.2598005 0.4050554

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Hist & Density par(mfrow=c(2,1)) hist(fdeaths/mdeaths, nclass=30) plot(density(fdeaths/mdeaths))

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Data Frames help(cars) names(cars) summary(cars) plot(cars) cars2 = cars cars2$speed2 = cars$speed^2 cars2$speed3 = cars$speed^3 summary(cars2) names(cars2) plot(cars2) options(digits=2) cor(cars2)

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Normality par(mfrow=c(2,1)) plot(density(cars$dist/cars$sp eed)) lines(density(rnorm(1000000, mean(cars$dist/cars$spe ed), sqrt(var(cars$dist/ cars$speed)))), col="red") qqnorm(cars$dist/cars$speed ) abline(mean(cars$dist/cars$s peed), sqrt(var(cars$dist/cars$s peed)))

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Stopping Distance Increases Quickly With Speed plot(cars$speed, cars$dist/cars$speed) boxplot(split(cars$dist/cars$sp eed, round(cars$speed/10)*10))

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Quadratic Model of Stopping Distance plot(cars$speed, cars$dist) cars$speed2 = cars$speed^2 g2 = glm(cars$dist ~ cars$speed2) lines(cars$speed, g2$fitted.values)

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Bowed Residuals g1 = glm(dist ~ poly(speed, 1), data=cars) g2 = glm(dist ~ poly(speed, 2), data=cars) par(mfrow=c(1,2)) boxplot(split(g1$resid, round(cars$speed/5))); abline(h=0) boxplot(split(g2$resid, round(cars$speed/5))); abline(h=0)

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Help, Demo, Example demo(graphics) example(plot) example(lines) help(cars) help(WWWusage) example(abline) example(text) example(par) boxplots example(boxplot) help(chickwts) demo(plotmath) pairs example(pairs) help(quakes) help(airquality) help(attitude) Anorexia utils::data(anorexia, package="MASS") pairs(anorexia, col=c("red", "green", "blue")[anorexia$Treat]) counting example(table) example(quantile) example(hist) help(faithful)

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Randomness example(rnorm) example(rbinom) example(rt) Normality example(qqnorm) Regression help(cars) example(glm) demo(lm.glm)