Stat 511
Homework 6 PMD solution
Spring 2011
Note: These are sketchy because I’m short of time and Yun has more important things to worry
about. They give you a sense of my answers. I will return HW before the midterm if I get it from
Yun.
1. The data in bacteria.txt are from a study of bacterial growth as a function of sugar concen
tration in the growth medium. This is a completely randomized design with five replicates of
four sugar concentrations (1gm/ml, 2gm/ml, 3gm/ml, and 4gm/ml). The investigators want
to know 1) whether sugar concentration affects bacterial growth and 2) does a simple model
describe the relationship between sugar concentration and growth. Please analyze the data in
an appropriate manner, using orthogonal polynomials, and briefly answer the investigator’s
two questions. The orthogonal polynomial coefficients for four equally spaced groups are:
X
linear
quadratic
cubic
1
3
1
1
2
1
1
3
3
1
1
3
4
3
1
1
If you plot the data, or fit a model and look at a residual plot, you see quickly that the equal
variance assumption is not appropriate. A plot of log variance vs log mean (a BoxCox plot,
from 500), indicates a log transformation is appropriate. So does looking at the residuals on
the log scale. Working with
Y
= log
grow
, I get:
1) Yes, the 3 d.f. F statistic comparing the 3 sugar levels is 49.3, with a pvalue of
<<
0.0001.
Growth is fastest when sugar = 1 and declines with increasing sugar concentration.
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 Spring '08
 Staff
 Regression Analysis, Error SS, sugar concentration, Yun, SSE model SS

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