Statistics Forestry Horticulture 572 Course website TA Email Website of TA Office Office hour Phone 1 Discussion 2 http www stat wisc edu courses st572 larget Xu He Mario hexu stat wisc edu www stat wisc edu hexu 1275F MSC Th 11 00 12 00 4 00 6 00 608 334 9792 Problem 1 The following data is collected to study the relationship between frequency of chirps made by a ground cricket and the corresponding ground temperature The frequency is measured as the number 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 1 temperature 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 plot chirps versus temperature including a regression line in the plot Is a simple linear regression model reasonable to predict the frequency of chirps from the temperature 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 temperature is 88 F d What are the estimated standard errors for the slope and intercept e What is a typical distance for the actual chirp frequency 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 14 temp 0 22 0 04 n 15 k 2 residual sd 0 98 R Squared 0 70 summary lm0 1 Call lm formula chirp temp data chirps Residuals Min 1Q 1 7411 0 5812 Median 0 0296 3Q 0 5825 Max 1 5061 Coefficients Estimate Std Error t value Pr t Intercept 0 6152 3 1443 0 2 0 84790 temp 0 2157 Signif codes 0 0392 5 5 0 00010 0 0 001 0 01 0 05 0 1 1 Residual standard error 0 98 on 13 degrees of freedom Multiple R Squared 0 7 Adjusted R squared 0 677 F statistic 30 3 on 1 and 13 DF p value 0 000102 2 Problem 2 A study was conducted to investigate the relationship between the size of the ants and the distance at which they foraged Ants were collected at various distance from the colony and measured Head width is measured in mm and utilized as a good indicator of an ant s size Distance is measured in meters and indicates how far the mound is from places where they were captured while foraging head width 1 895 1 811 1 179 1 684 1 937 1 768 distance 1 1 4 4 7 7 colony 1 2 1 2 1 2 Construct the matrix X for a multiple regression model to predict the ant size from colony and distance 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 with levels 1 and 2 2 20 19 chirp 18 17 16 15 14 70 75 80 85 temp 3 90
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