ST495/590 Assignment 1

ST495/590 Assignment 1 - Solutions
2a Create a table with the overall mean, standard deviation, and percent missing.
The following table provides the summary statistics for the ozone data.
Mean1
51.27
SD Percent Missing
17.26
4.32%
2b Create scatter plots of each pair of these variables
For this problem I computed the mean, standard deviation, and percent missing for
ozone at each of the n = 1, 106 locations, and constructed histograms of the n values
for each of the three summary measures (top row) and scatter plots for each pair
of summary measures (bottom row). The results show that the means and standard
deviations are right-skewed, the proportion of missing values is near zero for most sites,
and that site with large mean also tend to have large variance.
2c Conduct a linear regression with response equal to the sites mean and the sites variance and
percent missing as covariates
The results of the linear regression are in the table below. The regression suggests a
positive relationship between X and Y and a negative relationship between X and Z.
Intercept
Variance
Percent Missing (%)
Estimate
48.59
0.017
-0.105
1
Standard error
0.633
0.0030
0.036
p-value
< 0.0001
< 0.0001
0.036
0.15
0.005
60
80
100
0.00
0.000
0.00
40
0
500
40
60
Mean
80
100
40
80
100
100
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Percent Missing (%)
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20
20
Percent Missing (%)
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500
0
Variance
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100
Mean
Variance
0.10
Density
0.001
0.05
0.002
Density
0.003
0.004
0.04
0.03
0.02
0.01
Density
20
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0
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1500
Variance