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Microexam 3: Solutions
1. Model 1:
lm(formula = Prop_exotic ~
GDP + M_imports + GDP:M_imports
, data = exotic_sp)
Coefficients:
Estimate
Std. Error
t value
Pr(>t)
(Intercept)
5.124e02
4.111e02
1.247
0.226287
GDP
1.334e06
4.713e06
0.283
0.779920
M_imports
1.114e03
1.009e03
1.103
0.282385
GDP:M_imports
5.607e07
1.391e07
4.029
0.000606 ***

Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.07758 on 21 degrees of freedom
(1 observation deleted due to missingness)
Multiple RSquared: 0.7386, Adjusted Rsquared:
0.7013
Fstatistic: 19.78 on 3 and 21 DF,
pvalue: 2.514e06
> extractAIC(LinearModel.22)
[1]
4.00
124.18
Prop_exotic =
β
0
+
β
1
*GDP +
β
2
*M_imports +
β
3
*GDP*M_imports +
ε
b
0
= 5.12e02, pvalue = 0.226
b
1
= 1.33e06, pvalue = 0.780
b
2
= 1.11e03, pvalue = 0.282
b
3
= 5.61e07, pvalue = 0.000606
pvalue for the whole model: 2.51e06
For this model, the only parameter estimate that is significantly different than zero is the interaction between
GDP and M_imports.
2. GDP is the percapita Gross Domestic Product in dollars and M_imports is Merchandise imports as
percentage of GDP.
Multiplying these together results in a value that is related to the number of dollars
spent on imports (since the percentage is reported in numbers out of a hundred, to get dollars you need to
divide this product by 100).
Imports can be a source of exotic species so the more money a country spends
on imports could mean there is a greater chance of introducing invasive species to the country through
importing goods.
3. I would feel justified removing both GDP and M_imports because they both have large pvalues in Model
1.
Thinking about the variables themselves, I think it would make the most sense to remove M_imports
because the interaction term has information about the actual amount/value of imports rather than just its
percentage of the GDP.
I would test this by removing each variable separately and see if it made the model
better or worse.
Compared to Model 1, removing only M_imports (Model 2), slightly decreases the
adjusted R
2
value (from 0.7013 to 0.6983).
This leads me to believe that removing this variable definitely
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 Spring '08
 KENDALL,BERKLEY
 Environmental Science

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