Reading data (Creating a dataframe)

• mydata=read.csv(file=file.choose())
• mydata=read.table(file=file.choose()) #use to read in the txt files for the textbook exercises
• mydata=read.csv(P:/data/math/hartlaub/dataanalysis/Day1.csv") #reading csv file from Data Analysis folder into RStudio

• mydata #shows the entire data set
• head(mydata) #shows the first 6 rows
• tail(mydata) #shows the last 6 rows
• str(mydata) #shows the variable names and types
• names(mydata) #shows the variable names
• rename(V1,Variable1, dataFrame=mydata) #renames V1 to Variable1; Note that epicalc package must be installed!
• ls() #shows a list of objects that are available
• attach(mydata) #attaches the dataframe to the R search path, which makes it easy to access variable names

• mean(x) #computes the mean of the variable x
• median(x) #computes the median of the variable x
• sd(x) #computes the standard deviation of the variable x
• IQR(x) #computer the IQR of the variable x
• summary(x) #computes the 5-number summary and the mean of the variable x
• t.test(x) #get a one sample t test
• t.test(x,y) #get a two sample t test
• t.test(x, y, paired=TRUE) #get a paired t test
• cor(x,y) #computes the correlation coefficient
• cor(mydata) #computes a correlation matrix
• cor.test(x,y) #test plus CI for rho

Graphical Displays

• windows(record=TRUE) #records your work, including plots
• hist(x) #creates a histogram for the variable x
• boxplot(x) # creates a boxplot for the variable x
• boxplot(y~x) # creates side-by-side boxplots
• stem(x) #creates a stem plot for the variable x
• plot(y~x) #creates a scatterplot of y versus x
• plot(mydata) #provides a scatterplot matrix
• abline(lm(y~x)) #adds regression line to plot
• lines(lowess(x,y)) # adds lowess line (x,y) to plot
• qplot(x, y) #creates a quick plot (ggplot2 package must be installed)
• ci.plot(regmodel) #creates a scatterplot with fitted line, confidence bands, and prediction bands (HH package must be installed)

Liner Regression Models

• regmodel=lm(y~x) #fit a regression model
• summary(regmodel) #get results from fitting the regression model
• anova(regmodel) #get the ANOVA table fro the regression fit
• plot(regmodel) #get four plots, including normal probability plot, of residuals
• fits=regmodel$fitted #store the fitted values in variable named "fits"
• resids=regmodel$residuals #store the residual values in a varaible named "resids"
• sresids=rstandard(regmodel) #store the standardized residuals in a variable named "sresids"
• studresids=rstudent(regmodel) #store the studentized residuals in a variable named "studresids"
• beta1hat=regmodel$coeff[2] #assign the slope coefficient to the name "beta1hat"
• qt(.975,15) # find the 97.5% percentile for a t distribution with 15 df
• confint(regmodel) #CIs for all parameters
• newx=data.frame(X=41) #create a new data frame with one new x* value of 41
• predict.lm(regmodel,newx,interval="confidence") #get a CI for the mean at the value x*
• predict.lm(model,newx,interval="prediction") #get a prediction interval for an individual Y value at the value x*
• hatvalues(regmodel) #get the leverage values (hi)
• Diagnostics
  • sresids=rstandard(regmodel) #store the standardized residuals in a variable named "sresids"
  • standresid=stdres(regmodel) #store the standardized residuals in a variable named "standresids"
  • stud.del.resids=rstudent(regmodel) #store the studentized deleted residuals in a variable named "stud.del.resids"
  • hatvalues(regmodel) #get the leverage values (hi)
  • cooks.distance(regmodel) #get Cook's distance
  • dfbetas(regmodel) #print all dfbetas
  • dfbetas(regmodel)[4,1] #dfbeta for case 4, first coefficient (i.e., b_0)
  • dffits(regmodel) [4] #dffits for case 4
  • influence(regmodel) #various influence statistics, including hat values and dfbeta (not dfbetas) values
  • library(car) #load the package car
    • vif(regmodel) #variance inflation factors
    • avPlots(regmodel) #added variable plot
• Tests for homogeneity of variance
  • bptest(regmodel) #get the Breusch-Pagan test (lmtest package must be installed)
  • levene.test(Y, groupvariable) #get the Levene test (lawstat package must be installed)
• Tests for normality
  • ad.test(resids) #get Anderson-Darling test for normality (nortest package must be installed)
  • cvm.test(resids) #get Cramer-von Mises test for normaility (nortest package must be installed)
  • lillie.test(resids) #get Lilliefors (Kolmogorov-Smirnov) test for normality (nortest package must be installed)
  • pearson.test(resids) #get Pearson chi-square test for normaility (nortest package must be installed)
  • sf.test(resids) #get Shapiro-Francia test for normaility (nortest package must be installed)
• Lack-of-fit test
  • Reduced=lm(y~x)#fit reduced model
  • Full=lm(y~0+as.factor(x)) #fit full model
  • anova(Reduced, Full) #get lack-of-fit test
• boxcox(regmodel) #evaluate possible Box-Cox transformations (MASS package must be installed)
• Model Selection
  • library(leaps) #load the leaps package
  • allmods = regsubsets(y~x1+x2+x3+x4, nbest=2, data=mydata) #(leaps package must be loaded), identify best two models for 1, 2, 3 predictors
  • summary(allmods) # get summary of best subsets
  • summary(allmods)$adjr2 #adjusted R^2 for some models
  • summary(allmods)$cp #Cp for some models
  • plot(allmods, scale="adjr2") # plot that identifies models
  • plot(allmods, scale="Cp") # plot that identifies models
  • fullmodel=lm(y~., data=mydata) # regress y on everything in mydata
  • MSE=(summary(fullmodel)$sigma)^2 # store MSE for the full model
  • extractAIC(lm(y~x1+x2+x3), scale=MSE) #get Cp (equivalent to AIC)
  • step(fullmodel, scale=MSE, direction="backward") #backward elimination
  • step(fullmodel, scale=MSE, direction="forward") #forward elimination
  • step(fullmodel, scale=MSE, direction="both") #stepwise regression
  • none(lm(y~1) #regress y on the constant only
  • step(none, scope=list(upper=fullmodel), scale=MSE) #use Cp in stepwise regression

Logistic Regression

• table(y) #get a table of the distribution of y
• mytable=table(y, x) #get a 2-way table of y by x
• chisq.test(mytable) #Chi-sq test with Yates continuity correction
• chisq.test(mytable, correction=FALSE) #Chi-sq test of independence without Yates continuity correction
• prop.table(table(y, x),1) #get a table of row proportions
• prop.table(table(y, x),2) #get a table of column proportions
• prop.test(c(39,22), c(100,100), correction=FALSE) #2-sample proportion test without Yates continuity correction
• plot(x,jitter(y,amount=0.05)) #jitter y in the plot
• anova(reducedmodel, fullmodel, test="Chisq") #nested G test
• drop1(mymodel, test="Chisq") #G tests to see what to drop next
• as.factor(X) #create dummy variables for the levels of the variable X
• model1=glm(y~as.factor(X), family=binomial) #fit model with the categories of X as predictors
• summary(model1) #gives Z tests, residual deviance, and null deviance
• anova(model1, test="Chisq") #test of H0: constant term is all that is needed. (i.e., nested G test against the model y~1.)
• confint(model1) #CIs for all parameters
• confint(model1, parm="x") #CI for the coefficient of x
• exp(confint(model1, parm="x")) #CI for odds ratio
• shortmodel=glm(cbind(y1,y2)~x, family=binomial) binomial inputs
• dresid=residuals(model1, type="deviance") #deviance residuals
• presid=residuals(model1, type="pearson") #Pearson residuals
• plot(residuals(model1, type="deviance")) #plot of deviance residuals
• newx=data.frame(X=20) #set (X=20) for an upcoming prediction
• predict(mymodel, newx, type="response") #get predicted probability at X=20

Analysis of Variance

• t.test(y~x, var.equal=TRUE) #pooled t-test where x is a factor
• x=as.factor(x) #coerce x to be a factor variable
• tapply(y, x, mean) #get mean of y at each level of x
• tapply(y, x, sd) #get stadard deviations of y at each level of x
• tapply(y, x, length) #get sample sizes of y at each level of x
• library(gplots) #load gplots package
  • plotmeans(y~x) #means and 95% confidence intervals
• AOVmodel=aov(y~x) #one-way ANOVA
• summary(AOVmodel) #get ANOVA output
• oneway.test(y~x, var.equal=TRUE) #one-way test output
• library(car) #load car package
  • levene.test(y,x) #Levene's test for equal variances
• blockmodel=aov(y~x+block) #Randomized block design model with "block" as a variable
• tapply(lm(y~x1:x2,mean) #get the mean of y for each cell of x1 by x2
• anova(lm(y~x1+x2)) #a way to get a two-way ANOVA table
• interaction.plot(FactorA, FactorB, y) #get an interaction plot
• pairwise.t.test(y,x,p.adj="none") #pairwise t tests
• pairwise.t.test(y,x,p.adj="bonferroni") #pairwise t tests
• TukeyHSD(AOVmodel) #get Tukey CIs and P-values
• plot(TukeyHSD(AOVmodel)) #get 95% family-wise CIs
• library(multcomp) #load multcomp package
  • contrast=rbind(c(.5,.5,-1/3,-1/3,-1/3)) #set up a contrast
  • summary(glht(AOVmodel, linfct=mcp(x=contrast))) #test a contrast
  • confint(glht(AOVmodel, linfct=mcp(x=contrast))) #CI for a contrast
• kruskal.test(y~x) #Kruskal-Wallis test
• friedman.test(y,x,block) #Friedman test for block design