Statistics/Forestry/Horticulture 572 Discussion 2Course website http://www.stat.wisc.edu/courses/st572-larget/TA Xu He(Mario)Email [email protected] of TA www.stat.wisc.edu/∼hexuOffice 1275F, MSCOffice hour Th 11:00-12:00, 4:00-6:00Phone (608)334-97921 Problem 1The following data is collected to study the relationship between frequency of chirps made by aground cricket and the corresponding ground temperature. The frequency is measured as the num-ber of wing vibrations per second.chirps (/second) 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 14.1temperature (F) 88.6 71.6 93.3 84.3 80.6 75.2 69.7 82.0 69.4 83.3 78.6 82.6 80.6 83.5 76.3(a) Use xyplot() in lattice package to p lot chirps versus temperature, including a regression line inthe plot.Is a simple linear regression model reasonable to predict the frequency of chirps from the temper-ature?(b) Use lm() to fit this model. What are the slope and intercept of the model?(c) Use this model to predict chirp frequency under similar conditions when the temperatureis 88 F.(d) What are the estimated standard errors for the slope and intercept?(e) What is a typical distance for the actual chirp fr equ en cy to differ from the predicted frequency?Answer:> chirps=read.table("chirps.txt",header=T)> xyplot(chirp~temp,data=chirps,type=c("p","r"))>> lm0=lm(chirp~temp,chirps)> display(lm0)lm(formula = chirp ~ temp, data = chirps)coef.est coef.se(Intercept) -0.62 3.14temp 0.22 0.04---n = 15, k = 2 residual sd = 0.98, R-Squared = 0.70> summary(lm0)1Call: lm(formula = chirp ~ temp, data = chirps)Residuals:Min 1Q Median 3Q Max-1.7411 -0.5812 0.0296 0.5825 1.5061Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) -0.6152 3.1443 -0.2 0.84790temp 0.2157 0.0392 5.5 0.00010 ***Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1Residual standard error: 0.98 on 13 degrees of freedom MultipleR-Squared: 0.7, Adjusted R-squared: 0.677 F-statistic: 30.3on 1 and 13 DF, p-value: 0.0001022 Problem 2A study was conducted to investigate the relationship between the size of the ants and the distanceat which they foraged. Ants were collected at various distance from the colony and measured. Headwidth is measured in mm and utilized as a good ind icator of an ant’s s ize. Distance is measured inmeters and indicates how far the mound is from places where they were captured while foraging.head width distance colony1.895 1 11.811 1 21.179 4 11.684 4 21.937 7 11.768 7 2Construct the matrix X for a multiple regression model to predict the ant size from colony anddistance if:(a) Distance is treated as quantitative and colony is treated as a factor with levels 1 and 2.(b) Distance is treated as a factor with levels 1, 4, and 7, and colony is treated as a factor withlevels 1 and 2.2tempchirp1415161718192070 75 80 85
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