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Stat 200
Homework 3 Solutions
On Your Own #
a) Our best guess for the weight is the class mean and you are likely to be off by the standard deviation.
b) β 1 = r(Sy/Sx) = .5(23.27/3.97) = 2.
β 0 = Y − β 1 X = 158.71− 2.93* 69.47 = -44.
weight = -44.8371 + 2.93*height
c) -44.8371 + 2.93*70 = 160.263 pounds
Se = 1 − r^2 * Sy = 1 − .5^2 * 23.27 = 20.
d) predicted weight: -44.8371 + 2.93*74 = 171.9829 = W residuals: 161 – W = -10.98 180 – W = 8.02 190 – W = 18.
3.2 …Enter in the data and then recreate the table. Make a segmented barplot showing the amount of spam and the total amount of e-mail.
Solution
spam <- matrix(c(50,125,110,210,225,375,315,475,390,590,450,700), nrow=2) rownames(spam) <- c("spam", "total") colnames(spam) <- c("2000", "2001", "2002", "2003", "2004", "2005") spam 2000 2001 2002 2003 2004 2005 spam 50 110 225 315 390 450 total 125 210 375 475 590 700
barplot(spam, main="Volume of spam in commercial e-mail (in billions)")
2000 2001 2002 2003 2004 2005
Volume of spam in commercial e-mail (in billions)
0
200
400
600
800
3.8 …Create side-by-side boxplots of the variable reaction.time (Using R) for the two values of control. Compare the centers and spreads.
Solution ~ load R package UsingR.
attach(reaction.time) C <- time[which(control=="C")] T <- time[which(control=="T")] boxplot(C,T, names=c("No cell phone", "Cell phone"))
No cell phone Cell phone
In comparing the two boxplots answers may vary. As long as something was mentioned about the center and spread are shifted by what appears to be a good amount. No cell phone usage has a faster time response than cell phone usage.
3.10 The data set stud.recs (UsingR) contains 160 SAT scores for incoming college students stored in the variables sat.v and sat.m. Produce side-by-side densityplots of the data. Do the two data sets appear to have the same center? Then make a quantile- quantile plot. Do the data sets appear to have the same shape?
Solution ~load R package UsingR
attach(stud.recs) plot(density(sat.v), ylim=c(0,0.006), main="densityplots of Verbal and Math SAT scores") lines(density(sat.m), lty=2)
batted in. What is his predicted number of RBIs based on his number of home runs? What is his residual?
Solution ~load R package Using R
model <- lm(RBI~HR, data=batting) plot(batting$HR, batting$RBI) abline(model)
batting$HR
batting$RBI
predict(model, data.frame(HR=33)) [1] 104.
104.1099 - 98 [1] 6.
