l10 - STAT 350 Fall 2008 DUE: Friday, December 12th @ 4:30...

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STAT 350 – Fall 2008 Lab #10 Solution DUE: Friday, December 12 th @ 4:30 p.m. For her senior thesis, an undergraduate in biology wanted to study the effect of crowding (population density) on fecundity (egg production) using Tribolium (flour) beetles. She had 80 jars of flour. She controlled the density (number of beetles per jar) in her experiment and then would measure the number of eggs produced. Dividing the number of eggs by the number of adults would give a measure of the fecundity of the population (she decided it would be impossible to sex all the beetles which is why she is not measuring fecundity as #eggs per female). She used density levels ranging from 100 to 2000 beetles per jar and replicated each density level 4 times. The results of her experiment are given in the accompanying Excel file. Unless otherwise indicated, all plots and analyses for this lab are to be done using SAS. Please put all SAS input (contents of the editor window) and all SAS output (contents of the Output window) as an appendix. Nothing pasted directly from SAS should be given as an answer to the questions below ( except for graphs )! 1. This part should not be done in SAS . One thing that she is interested in is estimating the fecundity when the population density is 1000. Using the 4 observations for fecundity when density was 1000, give a point estimate for the predicted # eggs/female and give a 90% prediction interval (be sure to show your work). Consider this early review – this has nothing to do with regression . The 4 fecundities with density = 1000, were 1.32, 1.14, 1.45, and 1.37 the average of these 4 fecundities is 1.32, the standard deviation is 0.131403 The sum of the 4 observations is 5.28, the sum of the squares is 7.0214 SS yy = 7.0214 – 5.28 2 /4 = 0.0518 90% PI: N 1 1.32 2.353 0.131403 1 4 with df=3 t ±+ 0.97431 to 1.66569 2. No transformations: Use density as the independent variable ( x ) and fecundity as the dependent variable ( y ). a. Using SAS, find the least squares regression equation to predict fecundity from density. ˆ 4.79201 0.00254 f d =− b. Using SAS, give a point estimate for the predicted fecundity (# eggs/female) and give a 90% prediction interval for the fecundity (# of eggs/adult) when the density is 1000. Point Estimate: 2.2505 90% PI: 0.5002 to 4.0007 Lab #10 Solution Page 1 of 13
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c. Is this regression "significant"? Give the value of the appropriate test statistic, along with its degrees of freedom. Yes. F = 157.37, df 1 = 1, df 2 = 78, p < 0.0001 OR Yes. t = -12.55, df = 78, p < 0.0001 d. Using the plot option in PROC REG, give a scatter plot of fecundity versus density with the fitted regression line. f ecundi t y = 4. 792 - 0. 0025 densi t y N 80 Rsq 0. 6686 Adj Rsq 0. 6644 RMSE 1. 0449 0 1 2 3 4 5 6 7 8 9 densi t y 0 250 500 750 1000 1250 1500 1750 2000 e. Using the plot option in PROC REG, give the residual plot from this regression analysis. What does this plot tell you about your analysis? N 80 -2 -1 0 1 2 3 4 0 Lab #10 Solution Page 2 of 13
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f. Using PROC UNIVARIATE, give a Q-Q plot of the residuals. What does this plot tell you about your analysis?
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This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue University.

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l10 - STAT 350 Fall 2008 DUE: Friday, December 12th @ 4:30...

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