Microexam 3 (HAB solutions)

Microexam 3 (HAB solutions) - Microexam 3 Solutions 1 Model...

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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) 5.124e-02 4.111e-02 1.247 0.226287 GDP 1.334e-06 4.713e-06 0.283 0.779920 M_imports -1.114e-03 1.009e-03 -1.103 0.282385 GDP:M_imports 5.607e-07 1.391e-07 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 R-Squared: 0.7386, Adjusted R-squared: 0.7013 F-statistic: 19.78 on 3 and 21 DF, p-value: 2.514e-06 > 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 = 5.12e-02, p-value = 0.226 b 1 = 1.33e-06, p-value = 0.780 b 2 = -1.11e-03, p-value = 0.282 b 3 = 5.61e-07, p-value = 0.000606 p-value for the whole model: 2.51e-06 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 per-capita 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 p-values 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).
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