Dana Drakulich Stat 467 HW 13

1.)11.2.1. Crickets make their chirping sound by sliding one wing cover very rapidly back and forth over the other. Biologists have long been aware that there is a linear relationship between temperature and the frequency with which a cricket chirps, although the slope and y-intercept of the relationship vary from species to species. The following table lists fifteen frequency-temperature observations recorded for the striped ground cricket, Nemobius fasciatus fasciatus(145). Plot these data and find the equation of the least squares line, y = a+bx. Suppose a cricket of this species is observed to chirp eighteen times per second. What would be the estimated temperature? For the data in the table, the sums needed are:

x = c(20.0, 16.0, 19.8, 18.4, 17.1, 15.5, 14.7, 17.1, 15.4, 16.2, 15.0, 17.2, 16.0, 17.0, 14.4)

y = c(88.6, 71.6, 93.3, 84.3, 80.6, 75.2, 69.7, 82.0, 69.4, 83.3, 79.6, 82.6, 80.6, 83.5, 76.3)

plot(x, y, xlab="Chirps per Sec", ylab="Temp", main="Regerssion Plot", pch=15)
abline(lm(y~x), col = "blue")

2.)11.2.3. As water temperature increases, sodium nitrate (NaNO3) becomes more soluble. The following table (110) gives the number of parts of sodium nitrate that dissolve in one hundred parts of water.

x = c(0, 4, 10, 15, 21, 29, 36, 51, 68)
y = c(66.7, 71.0, 76.3, 80.6, 85.7, 92.9, 99.4, 113.6, 125.1)

p <- lm(y~x)
resid(p)
##            1            2            3            4            5            6 
## -0.807794198  0.009644226  0.085801861  0.032599891 -0.091242474  0.143634373 
##            7            8            9 
##  0.549151615  1.689545703 -1.611340996
qqnorm(resid(p), xlab="Temp, x", ylab="Residuals")

4.) 11.2.9). An Atomic Energy Commission nuclear facility was established in Hanford, Washington, in 1943. Over the years, a significant amount of strontium 90 and cesium 137 leaked into the Columbia River. In a study to determine how much this radioactivity caused serious medical problems for those who lived along the river, public health officials created an index of radioactive exposure for nine Oregon counties in the vicinity of the river. As a covariate, cancer mortality was determined for each of the counties (45). The results are given in the table in the next column. For the nine (xi, yi)’s in the table,

x = c(2.49, 2.57, 3.41, 1.25, 1.62, 3.83, 11.64, 6.41, 8.34)
y = c(147.1, 130.1, 129.9, 113.5, 137.5, 162.3, 207.5, 177.9, 210.3)

cm <- lm(y~x)
resid(cm)
##          1          2          3          4          5          6          7 
##   9.398043  -8.340473 -16.294897 -12.754951   7.829410  12.227892 -14.669782 
##          8          9 
##   4.010734  18.594024
qqnorm(resid(cm), xlab="Temp, x", ylab="Residuals")